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A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-18 Umut Bektaş, Halil Anaç
This paper solves fractional differential equations using the Shehu transform in combination with the q-homotopy analysis transform method (q-HATM). As the Shehu transform is only applicable to linear equations, q-HATM is an efficient technique for approximating solutions to nonlinear differential equations. In nonlinear systems that explain the emergence of stripes in 2D systems, the Newell–Whitehead–Segel
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Existence and multiplicity of solutions for fractional \(p_{1}(x,\cdot )\& p_{2}(x,\cdot )\)-Laplacian Schrödinger-type equations with Robin boundary conditions Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-13 Zhenfeng Zhang, Tianqing An, Weichun Bu, Shuai Li
In this paper, we study fractional $p_{1}(x,\cdot )\& p_{2}(x,\cdot )$ -Laplacian Schrödinger-type equations for Robin boundary conditions. Under some suitable assumptions, we show that two solutions exist using the mountain pass lemma and Ekeland’s variational principle. Then, the existence of infinitely many solutions is derived by applying the fountain theorem and the Krasnoselskii genus theory
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Blow-up and lifespan of solutions for elastic membrane equation with distributed delay and logarithmic nonlinearity Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-08 Salah Boulaaras, Rashid Jan, Abdelbaki Choucha, Aderrahmane Zaraï, Mourad Benzahi
We examine a Kirchhoff-type equation with nonlinear viscoelastic properties, characterized by distributed delay, logarithmic nonlinearity, and Balakrishnan–Taylor damping terms (elastic membrane equation). Under appropriate hypotheses, we establish the occurrence of solution blow-up.
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Caputo fractional backward stochastic differential equations driven by fractional Brownian motion with delayed generator Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-07 Yunze Shao, Junjie Du, Xiaofei Li, Yuru Tan, Jia Song
Over the years, the research of backward stochastic differential equations (BSDEs) has come a long way. As a extension of the BSDEs, the BSDEs with time delay have played a major role in the stochastic optimal control, financial risk, insurance management, pricing, and hedging. In this paper, we study a class of BSDEs with time-delay generators driven by Caputo fractional derivatives. In contrast to
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Positive solutions for a semipositone anisotropic p-Laplacian problem Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-01 A. Razani, Giovany M. Figueiredo
In this paper, a semipositone anisotropic p-Laplacian problem $$ -\Delta _{\overrightarrow{p}}u=\lambda f(u), $$ on a bounded domain with the Dirchlet boundary condition is considered, where $A(u^{q}-1)\leq f(u)\leq B(u^{q}-1)$ for $u>0$ , $f(0)<0$ and $f(u)=0$ for $u\leq -1$ . It is proved that there exists $\lambda ^{*}>0$ such that if $\lambda \in (0,\lambda ^{*})$ , then the problem has a positive
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Optimal decay-in-time rates of solutions to the Cauchy problem of 3D compressible magneto-micropolar fluids Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-29 Xinyu Cui, Shengbin Fu, Rui Sun, Fangfang Tian
This paper focuses on the long time behavior of the solutions to the Cauchy problem of the three-dimensional compressible magneto-micropolar fluids. More precisely, we aim to establish the optimal rates of temporal decay for the highest-order spatial derivatives of the global strong solutions by the method of decomposing frequency. Our result can be regarded as the further investigation of the one
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Generalized strongly n-polynomial convex functions and related inequalities Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-26 Serap Özcan, Mahir Kadakal, İmdat İşcan, Huriye Kadakal
This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite–Hadamard inequality is established for generalized strongly n-polynomial convex functions. Additionally, new integral inequalities of Hermite–Hadamard type are derived for this class of functions
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Quasilinear Schrödinger equations with superlinear terms describing the Heisenberg ferromagnetic spin chain Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-23 Yongkuan Cheng, Yaotian Shen
In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain: $$ -\Delta u+V(x)u-\frac{u}{\sqrt{1-u^{2}}}\Delta \sqrt{1-u^{2}}=c \vert u \vert ^{p-2}u,\quad x\in \mathbb{R}^{N}, $$ where $2< p<2^{*}$ , $c>0$ and $N\geq 3$ . By the cutoff technique, the change of variables and the $L^{\infty}$ estimate, we prove that there exists $c_{0}>0$ , such that
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Upper and lower solutions method for a class of second-order coupled systems Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-23 Zelong Yu, Zhanbing Bai, Suiming Shang
This paper provides a class of upper and lower solution definitions for second-order coupled systems by transforming the fourth-order differential equation into a second-order differential system. Then, by constructing a homotopy parameter and utilizing the maximum principle, we propose an upper and lower solutions method for studying a class of second-order coupled systems with Dirichlet boundary
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The Robin problems for the coupled system of reaction–diffusion equations Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-23 Po-Chun Huang, Bo-Yu Pan
This article investigates the local well-posedness of Turing-type reaction–diffusion equations with Robin boundary conditions in the Sobolev space. Utilizing the Hadamard norm, we derive estimates for Fokas unified transform solutions for linear initial-boundary value problems subject to external forces. Subsequently, we demonstrate that the iteration map, defined by the unified transform solutions
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Existence and stability of a q-Caputo fractional jerk differential equation having anti-periodic boundary conditions Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-22 Khansa Hina Khalid, Akbar Zada, Ioan-Lucian Popa, Mohammad Esmael Samei
In this work, we analyze a q-fractional jerk problem having anti-periodic boundary conditions. The focus is on investigating whether a unique solution exists and remains stable under specific conditions. To prove the uniqueness of the solution, we employ a Banach fixed point theorem and a mathematical tool for establishing the presence of distinct fixed points. To demonstrate the availability of a
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Hybrid cubic and hyperbolic b-spline collocation methods for solving fractional Painlevé and Bagley-Torvik equations in the Conformable, Caputo and Caputo-Fabrizio fractional derivatives Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-20 Nahid Barzehkar, Reza Jalilian, Ali Barati
In this paper, we approximate the solution of fractional Painlevé and Bagley-Torvik equations in the Conformable (Co), Caputo (C), and Caputo-Fabrizio (CF) fractional derivatives using hybrid hyperbolic and cubic B-spline collocation methods, which is an extension of the third-degree B-spline function with more smoothness. The hybrid B-spline function is flexible and produces a system of band matrices
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Existence and multiplicity of solutions of fractional differential equations on infinite intervals Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-08 Weichen Zhou, Zhaocai Hao, Martin Bohner
In this research, we investigate the existence and multiplicity of solutions for fractional differential equations on infinite intervals. By using monotone iteration, we identify two solutions, and the multiplicity of solutions is demonstrated by the Leggett–Williams fixed point theorem.
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Existence of normalized solutions for Schrödinger systems with linear and nonlinear couplings Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-08 Zhaoyang Yun, Zhitao Zhang
In this paper we study the nonlinear Bose–Einstein condensates Schrödinger system $$ \textstyle\begin{cases} -\Delta u_{1}-\lambda _{1} u_{1}=\mu _{1} u_{1}^{3}+\beta u_{1}u_{2}^{2}+ \kappa (x) u_{2}\quad\text{in }\mathbb{R}^{3}, \\ -\Delta u_{2}-\lambda _{2} u_{2}=\mu _{2} u_{2}^{3}+\beta u_{1}^{2}u_{2}+ \kappa (x) u_{1}\quad\text{in }\mathbb{R}^{3}, \\ \int _{\mathbb{R}^{3}} u_{1}^{2}=a_{1}^{2},\qquad
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Infinitely many solutions for quasilinear Schrödinger equation with concave-convex nonlinearities Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-06 Lijuan Chen, Caisheng Chen, Qiang Chen, Yunfeng Wei
In this work, we study the existence of infinitely many solutions to the following quasilinear Schrödinger equations with a parameter α and a concave-convex nonlinearity: 0.1 $$\begin{aligned}& -\Delta _{p}u+V(x) \vert u \vert ^{p-2}u-\Delta _{p}\bigl( \vert u \vert ^{2\alpha}\bigr) \vert u \vert ^{2\alpha -2}u= \lambda h_{1}(x) \vert u \vert ^{m-2}u+h_{2}(x) \vert u \vert ^{q-2}u, \\& \quad x\in {\mathbb{R}}^{N}
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Infinite system of nonlinear tempered fractional order BVPs in tempered sequence spaces Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-01 Sabbavarapu Nageswara Rao, Mahammad Khuddush, Ahmed Hussein Msmali, Abdullah Ali H. Ahmadini
This paper deals with the existence results of the infinite system of tempered fractional BVPs $$\begin{aligned}& {}^{\mathtt{R}}_{0}\mathrm{D}_{\mathrm{r}}^{\varrho , \uplambda} \mathtt{z}_{\mathtt{j}}(\mathrm{r})+\psi _{\mathtt{j}}\bigl(\mathrm{r}, \mathtt{z}(\mathrm{r})\bigr)=0,\quad 0< \mathrm{r}< 1, \\& \mathtt{z}_{\mathtt{j}}(0)=0,\qquad {}^{\mathtt{R}}_{0} \mathrm{D}_{ \mathrm{r}}^{\mathtt{m}
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Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-26 Weiwei Zhao, Xiaoling Shao, Changhui Hu, Zhiyu Cheng
We establish a Liouville-type theorem for a weighted higher-order elliptic system in a wider exponent region described via a critical curve. We first establish a Liouville-type theorem to the involved integral system and then prove the equivalence between the two systems by using superharmonic properties of the differential systems. This improves the results in (Complex Var. Elliptic Equ. 5:1436–1450
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Blow-up solutions for a 4-dimensional semilinear elliptic system of Liouville type in some general cases Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-25 Sami Baraket, Anis Ben Ghorbal, Rima Chetouane, Azedine Grine
This paper is devoted to the existence of singular limit solutions for a nonlinear elliptic system of Liouville type under Navier boundary conditions in a bounded open domain of $\mathbb{R}^{4}$ . The concerned results are obtained employing the nonlinear domain decomposition method and a Pohozaev-type identity.
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Least energy nodal solutions for a weighted \((N, p)\)-Schrödinger problem involving a continuous potential under exponential growth nonlinearity Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-25 Sami Baraket, Brahim Dridi, Azedine Grine, Rached Jaidane
This article aims to investigate the existence of nontrivial solutions with minimal energy for a logarithmic weighted $(N,p)$ -Laplacian problem in the unit ball B of $\mathbb{R}^{N}$ , $N>2$ . The nonlinearities of the equation are critical or subcritical growth, which is motivated by weighted Trudinger–Moser type inequalities. Our approach is based on constrained minimization within the Nehari set
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New type of the unique continuation property for a fractional diffusion equation and an inverse source problem Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-23 Wenyi Liu, Chengbin Du, Zhiyuan Li
In this work, a new type of the unique continuation property for time-fractional diffusion equations is studied. The proof is mainly based on the Laplace transform and the properties of Bessel functions. As an application, the uniqueness of the inverse problem in the simultaneous determination of spatially dependent source terms and fractional order from sparse boundary observation data is established
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A necessary and sufficient condition for the existence of global solutions to reaction-diffusion equations on bounded domains Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-22 Soon-Yeong Chung, Jaeho Hwang
The purpose of this paper is to give a necessary and sufficient condition for the existence and non-existence of global solutions of the following semilinear parabolic equations $$ u_{t}=\Delta u+\psi (t)f(u),\quad \text{in }\Omega \times (0,\infty ), $$ under the mixed boundary condition on a bounded domain Ω. In fact, this has remained an open problem for a few decades, even for the case $f(u)=u^{p}$
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Existence and optimal controls of non-autonomous for impulsive evolution equation without Lipschitz assumption Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-19 Lixin Sheng, Weimin Hu, You-Hui Su
In this paper, we investigate the existence of mild solutions as well as optimal controls for non-autonomous impulsive evolution equations with nonlocal conditions. Using the Schauder’s fixed-point theorem as well as the theory of evolution family, we prove the existence of mild solutions for the concerned problem. Furthermore, without the Lipschitz continuity of the nonlinear term, the optimal control
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On a composite obtained by a mixture of a dipolar solid with a Moore–Gibson–Thompson media Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-19 Marin Marin, Sorin Vlase, Denisa Neagu
Our study is dedicated to a mixture composed of a dipolar elastic medium and a viscous Moore–Gibson–Thompson (MGT) material. The mixed problem with initial and boundary data, considered in this context, is approached from the perspective of the existence of a solution to this problem as well as the uniqueness of the solution. Considering that the mixed problem is very complex, both from the point of
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Bifurcations, chaotic behavior, sensitivity analysis, and various soliton solutions for the extended nonlinear Schrödinger equation Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-19 Mati ur Rahman, Mei Sun, Salah Boulaaras, Dumitru Baleanu
In this manuscript, our primary objective is to delve into the intricacies of an extended nonlinear Schrödinger equation. To achieve this, we commence by deriving a dynamical system tightly linked to the equation through the Galilean transformation. We then employ principles from planar dynamical systems theory to explore the bifurcation phenomena exhibited within this derived system. To investigate
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Three solutions for fractional elliptic systems involving ψ-Hilfer operator Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-18 Rafik Guefaifia, Tahar Bouali, Salah Boulaaras
In this paper, using variational methods introduced in the previous study on fractional elliptic systems, we prove the existence of at least three weak solutions for an elliptic nonlinear system with a p-Laplacian ψ-Hilfer operator.
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A fixed point result on an extended neutrosophic rectangular metric space with application Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-18 Gunaseelan Mani, Maria A. R. M. Antony, Zoran D. Mitrović, Ahmad Aloqaily, Nabil Mlaiki
In this paper, we propose the notion of extended neutrosophic rectangular metric space and prove some fixed point results under contraction mapping. Finally, as an application of the obtained results, we prove the existence and uniqueness of the Caputo fractional differential equation.
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Novel results of Milne-type inequalities involving tempered fractional integrals Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-18 Fatih Hezenci, Hüseyin Budak, Hasan Kara, Umut Baş
In this current research, we focus on the domain of tempered fractional integrals, establishing a novel identity that serves as the cornerstone of our study. This identity paves the way for the Milne-type inequalities, which are explored through the framework of differentiable convex mappings inclusive of tempered fractional integrals. The significance of these mappings in the realm of fractional calculus
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Dynamical behavior of a degenerate parabolic equation with memory on the whole space Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-17 Rong Guo, Xuan Leng
This paper is concerned with the existence and uniqueness of global attractors for a class of degenerate parabolic equations with memory on $\mathbb{R}^{n}$ . Since the corresponding equation includes the degenerate term $\operatorname{div}\{a(x)\nabla u\}$ , it requires us to give appropriate assumptions about the weight function $a(x)$ for studying our problem. Based on this, we first obtain the
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Spectral element discretization of the time-dependent Stokes problem with nonstandard boundary conditions Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-10 Mohamed Abdelwahed, Nejmeddine Chorfi
This work deals with the spectral element discretization of the time-dependent Stokes problem in two- and three-dimensional domains. The boundary condition is defined on the normal component of the velocity and the tangential components of the vorticity. The discretization related to the time variable is processed by a Backward Euler method. We prove through a detailed numerical analysis the well-posedness
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Continuity and pullback attractors for a semilinear heat equation on time-varying domains Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-08 Mingli Hong, Feng Zhou, Chunyou Sun
We consider dynamics of a semilinear heat equation on time-varying domains with lower regular forcing term. Instead of requiring the forcing term $f(\cdot )$ to satisfy $\int _{-\infty}^{t}e^{\lambda s}\|f(s)\|^{2}_{L^{2}}\,ds<\infty $ for all $t\in \mathbb{R}$ , we show that the solutions of a semilinear heat equation on time-varying domains are continuous with respect to initial data in $H^{1}$ topology
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Sign-changing solutions for Kirchhoff-type variable-order fractional Laplacian problems Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-05 Jianwen Zhou, Yueting Yang, Wenbo Wang
In this paper, we are concerned with the Kirchhoff-type variable-order fractional Laplacian problems involving critical exponents and logarithmic nonlinearity. By using the constraint variational method, we show the existence of one least energy sign-changing solution. Moreover, we show that this energy is strictly larger than twice the ground energy.
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Time decay of solutions for compressible isentropic non-Newtonian fluids Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-03 Jialiang Wang, Han Jiang
In this paper, we consider the Cauchy problem of a compressible Navier–Stokes system of Eills-type non-Newtonian fluids. We investigate the time decay properties of classical solutions for the compressible non-Newtonian fluid equations. More specifically, we construct a new linearized system in terms of a combination of the solutions, and then we investigate the long-time behavior of the Cauchy problem
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Ground-state sign-changing homoclinic solutions for a discrete nonlinear p-Laplacian equation with logarithmic nonlinearity Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-02 Xin Ou, Xingyong Zhang
By using a direct non-Nehari manifold method from (Tang and Cheng in J. Differ. Equ. 261:2384–2402, 2016), we obtain an existence result of ground-state sign-changing homoclinic solutions that only changes sign once and ground-state homoclinic solutions for a class of discrete nonlinear p-Laplacian equations with logarithmic nonlinearity. Moreover, we prove that the sign-changing ground-state energy
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Existence and uniqueness of solutions for multi-order fractional differential equations with integral boundary conditions Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-02 Jian-Ping Sun, Li Fang, Ya-Hong Zhao, Qian Ding
In this paper, we consider the existence and uniqueness of solutions for the following nonlinear multi-order fractional differential equation with integral boundary conditions $$ \textstyle\begin{cases} ({}^{C}D_{0+}^{\alpha}u)(t)+\sum_{i=1}^{m}\lambda _{i}(t)({}^{C}D_{0+}^{\alpha _{i}}u)(t)+ \sum_{j=1}^{n}\mu _{j}(t)({}^{C}D_{0+}^{\beta _{j}}u)(t)\\ \quad{}+\sum_{k=1}^{p}\xi _{k}(t)({}^{C}D_{0+}^{\gamma
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Nodal solutions for Neumann systems with gradient dependence Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-02 Kamel Saoudi, Eadah Alzahrani, Dušan D. Repovš
We consider the following convective Neumann systems: $$ ( \mathrm{S} ) \quad \textstyle\begin{cases} -\Delta _{p_{1}}u_{1}+ \frac{ \vert \nabla u_{1} \vert ^{p_{1}}}{u_{1}+\delta _{1} }=f_{1}(x,u_{1},u_{2}, \nabla u_{1},\nabla u_{2}) & \text{in } \Omega , \\ -\Delta _{p_{2}}u_{2}+ \frac{ \vert \nabla u_{2} \vert ^{p_{2}}}{u_{2}+\delta _{2} }=f_{2}(x,u_{1},u_{2}, \nabla u_{1},\nabla u_{2}) & \text{in
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Periodic solutions for second-order even and noneven Hamiltonian systems Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-02 Juan Xiao, Xueting Chen
In this paper, we consider the second-order Hamiltonian system $$ \ddot{x}+V^{\prime}(x)=0,\quad x\in \mathbb{R}^{N}. $$ We use the monotonicity assumption introduced by Bartsch and Mederski (Arch. Ration. Mech. Anal. 215:283–306, 2015). When V is even, we can release the strict convexity hypothesis, which is used by Bartsch and Mederski combined with the monotonicity assumption. When V is noneven
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Ground state solutions for a kind of superlinear elliptic equations with variable exponent Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-02 Bosheng Xiao, Qiongfen Zhang
In this paper, we focus on the existence of ground state solutions for the $p(x)$ -Laplacian equation $$ \textstyle\begin{cases} -\Delta _{p(x)}u+\lambda \vert u \vert ^{p(x)-2}u=f(x,u)+h(x) \quad \text{in } \Omega , \\ u=0,\quad \text{on }\partial \Omega . \end{cases} $$ Using the constraint variational method, quantitative deformation lemma, and strong maximum principle, we proved that the above
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Extinction behavior and recurrence of n-type Markov branching–immigration processes Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-02 Junping Li, Juan Wang
In this paper, we consider n-type Markov branching–immigration processes. The uniqueness criterion is first established. Then, we construct a related system of differential equations based on the branching property. Furthermore, the explicit expression of extinction probability and the mean extinction time are successfully obtained in the absorbing case by using the unique solution of the related system
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Periodic dynamics of predator-prey system with Beddington–DeAngelis functional response and discontinuous harvesting Bound. Value Probl. (IF 1.7) Pub Date : 2023-12-15 Yingying Wang, Zhinan Xia
This paper investigates a delayed predator-prey model with discontinuous harvesting and Beddington–DeAngelis functional response. Using the theory of differential inclusion theory, the existence of positive solutions in the sense of Filippov is discussed. Under reasonable assumptions and periodic disturbances, the existence of positive periodic solutions of the model is studied based on the theory
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Hybrid interpolative mappings for solving fractional Navier–Stokes and functional differential equations Bound. Value Probl. (IF 1.7) Pub Date : 2023-12-14 Hasanen A. Hammad, Hassen Aydi, Doha A. Kattan
The purpose of this study is to establish fixed-point results for new interpolative contraction mappings in the setting of Busemann space involving a convex hull. To illustrate our findings, we also offer helpful and compelling examples. Finally, the theoretical results are applied to study the existence of solutions to fractional Navier–Stokes and fractional-functional differential equations as applications
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Existence theory and Ulam’s stabilities for switched coupled system of implicit impulsive fractional order Langevin equations Bound. Value Probl. (IF 1.7) Pub Date : 2023-12-12 Rizwan Rizwan, Fengxia Liu, Zhiyong Zheng, Choonkil Park, Siriluk Paokanta
In this work, a system of nonlinear, switched, coupled, implicit, impulsive Langevin equations with two Hilfer fractional derivatives is introduced. The suitable conditions and results are established to discuss existence, uniqueness, and Ulam-type stability results of the mentioned model, with the help of nonlinear functional analysis techniques and Banach’s fixed-point theorem. Furthermore, we examine
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Existence and multiplicity of solutions for boundary value problem of singular two-term fractional differential equation with delay and sign-changing nonlinearity Bound. Value Probl. (IF 1.7) Pub Date : 2023-12-08 Rulan Bai, Kemei Zhang, Xue-Jun Xie
In this paper, we consider the existence of solutions for a boundary value problem of singular two-term fractional differential equation with delay and sign-changing nonlinearity. By means of the Guo–Krasnosel’skii fixed point theorem and the Leray–Schauder nonlinear alternative theorem, we obtain some results on the existence and multiplicity of solutions, respectively.
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Boundary value problems of quaternion-valued differential equations: solvability and Green’s function Bound. Value Probl. (IF 1.7) Pub Date : 2023-11-27 Jie Liu, Siyu Sun, Zhibo Cheng
This paper is associated with Sturm–Liouville type boundary value problems and periodic boundary value problems for quaternion-valued differential equations (QDEs). Employing the theory of quaternionic matrices, we prove the conditions for the solvability of the linear boundary valued problem and find Green’s function.
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A generalized Darbo’s fixed point theorem and its applications to different types of hybrid differential equations Bound. Value Probl. (IF 1.7) Pub Date : 2023-11-22 Anupam Das, Sudip Deb, Rupanjali Goswami, Tazuddin Ahmed, Zeynab Izadi, Vahid Parvaneh
In this article, a generalization of Darbo’s fixed point theorem using a new contraction operator is obtained to solve our proposed hybrid differential and fractional hybrid differential equations in a Banach space. The applicability of our results with the help of a suitable example has also been shown.
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Existence of exponential attractors for the coupled system of suspension bridge equations Bound. Value Probl. (IF 1.7) Pub Date : 2023-11-22 Jun-dong Jin
In this paper, we investigate the asymptotic behavior of the coupled system of suspension bridge equations. Under suitable assumptions, we obtain the existence of exponential attractors by using the decomposing technique of operator semigroup.
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Existence and multiplicity of periodic solutions for a nonlinear resonance equation with singularities Bound. Value Probl. (IF 1.7) Pub Date : 2023-11-22 Xiumei Xing, Lingling Wang, Shaoyong Lai
We investigate a second-order periodic system with singular potential and resonance. Utilizing the main integral method and fixed point theorems, we establish the existence and multiplicity of periodic solutions with respect to time under certain assumptions on the unbounded or oscillatory term.
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Riemann problem for a \(2\times 2\) hyperbolic system with time-gradually-degenerate damping Bound. Value Probl. (IF 1.7) Pub Date : 2023-11-14 Shiwei Li
This paper is focused on the Riemann problem for a $2\times 2$ hyperbolic system of conservation laws with a time-gradually-degenerate damping. Two kinds of non-self-similar solutions involving the delta-shocks and vacuum are obtained using the variable substitution method. The generalized Rankine-Hugoniot relation and entropy condition are clarified for the delta-shock. Furthermore, the vanishing
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Enhanced shifted Jacobi operational matrices of derivatives: spectral algorithm for solving multiterm variable-order fractional differential equations Bound. Value Probl. (IF 1.7) Pub Date : 2023-11-14 H. M. Ahmed
This paper presents a new way to solve numerically multiterm variable-order fractional differential equations (MTVOFDEs) with initial conditions by using a class of modified shifted Jacobi polynomials (MSJPs). As their defining feature, MSJPs satisfy the given initial conditions. A key aspect of our methodology involves the construction of operational matrices (OMs) for ordinary derivatives (ODs) and
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On the global existence and analyticity of the mild solution for the fractional Porous medium equation Bound. Value Probl. (IF 1.7) Pub Date : 2023-11-14 Muhammad Zainul Abidin, Muhammad Marwan
In this research article we focus on the study of existence of global solution for a three-dimensional fractional Porous medium equation. The main objectives of studying the fractional porous medium equation in the corresponding critical function spaces are to show the existence of unique global mild solution under the condition of small initial data. Applying Fourier transform methods gives an equivalent
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Decay of the 3D Lüst model Bound. Value Probl. (IF 1.7) Pub Date : 2023-11-10 Ying Sheng
In this paper, we consider the time-decay rate of the strong solution to the Cauchy problem for the three-dimensional Lüst model. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. The $\dot{H}^{-s}$ ( $0\leq s<\frac{3}{2}$ ) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.
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Dynamical behavior of perturbed Gerdjikov–Ivanov equation through different techniques Bound. Value Probl. (IF 1.7) Pub Date : 2023-11-09 Hamood Ur Rehman, Ifrah Iqbal, M. Mirzazadeh, Salma Haque, Nabil Mlaiki, Wasfi Shatanawi
The objective of this work is to investigate the perturbed Gerdjikov–Ivanov (GI) equation along spatio-temporal dispersion which explains the dynamics of soliton dispersion and evolution of propagation distance in optical fibers, photonic crystal fibers (PCF), and metamaterials. The algorithms, namely hyperbolic extended function method and generalized Kudryashov’s method, are constructed to obtain
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Existence and multiplicity of solutions for the Cauchy problem of a fractional Lorentz force equation Bound. Value Probl. (IF 1.7) Pub Date : 2023-10-31 Xiaohui Shen, Tiefeng Ye, Tengfei Shen
This paper aims to deal with the Cauchy problem of a fractional Lorentz force equation. By the methods of reducing and topological degree in cone, the existence and multiplicity of solutions to the problem were obtained, which extend and enrich some previous results.
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Existence and nonexistence of solutions for an approximation of the Paneitz problem on spheres Bound. Value Probl. (IF 1.7) Pub Date : 2023-10-23 Kamal Ould Bouh
This paper is devoted to studying the nonlinear problem with slightly subcritical and supercritical exponents $(S_{\pm \varepsilon}): \Delta ^{2}u-c_{n}\Delta u+d_{n}u = Ku^{ \frac{n+4}{n-4}\pm \varepsilon}$ , $u>0$ on $S^{n}$ , where $n\geq 5$ , ε is a small positive parameter and K is a smooth positive function on $S^{n}$ . We construct some solutions of $(S_{-\varepsilon})$ that blow up at one critical
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Numerical solution of Bratu’s boundary value problem based on Green’s function and a novel iterative scheme Bound. Value Probl. (IF 1.7) Pub Date : 2023-10-23 Junaid Ahmad, Muhammad Arshad, Kifayat Ullah, Zhenhua Ma
We compute the numerical solution of the Bratu’s boundary value problem (BVP) on a Banach space setting. To do this, we embed a Green’s function into a new two-step iteration scheme. After this, under some assumptions, we show that this new iterative scheme converges to a sought solution of the one-dimensional non-linear Bratu’s BVP. Furthermore, we show that the suggested new iterative scheme is essentially
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Determination of rigid inclusions immersed in an isotropic elastic body from boundary measurement Bound. Value Probl. (IF 1.7) Pub Date : 2023-10-12 Mohamed Abdelwahed, Nejmeddine Chorfi, Maatoug Hassine
We study the determination of some rigid inclusions immersed in an isotropic elastic medium from overdetermined boundary data. We propose an accurate approach based on the topological sensitivity technique and the reciprocity gap concept. We derive a higher-order asymptotic formula, connecting the known boundary data and the unknown inclusion parameters. The obtained formula is interesting and useful
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A new weighted fractional operator with respect to another function via a new modified generalized Mittag–Leffler law Bound. Value Probl. (IF 1.7) Pub Date : 2023-10-06 Sabri T. M. Thabet, Thabet Abdeljawad, Imed Kedim, M. Iadh Ayari
In this paper, new generalized weighted fractional derivatives with respect to another function are derived in the sense of Caputo and Riemann–Liouville involving a new modified version of a generalized Mittag–Leffler function with three parameters, as well as their corresponding fractional integrals. In addition, several new and existing operators of nonsingular kernels are obtained as special cases
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On nonlinear fractional Choquard equation with indefinite potential and general nonlinearity Bound. Value Probl. (IF 1.7) Pub Date : 2023-10-05 Fangfang Liao, Fulai Chen, Shifeng Geng, Dong Liu
In this paper, we consider a class of fractional Choquard equations with indefinite potential $$ (-\Delta )^{\alpha}u+V(x)u= \biggl[ \int _{{\mathbb{R}}^{N}} \frac{M(\epsilon y)G(u)}{ \vert x-y \vert ^{\mu}}\,\mathrm{d}y \biggr]M( \epsilon x)g(u), \quad x\in {\mathbb{R}}^{N}, $$ where $\alpha \in (0,1)$ , $N> 2\alpha $ , $0<\mu <2\alpha $ , ϵ is a positive parameter. Here $(-\Delta )^{\alpha}$ stands
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Computing Dirichlet eigenvalues of the Schrödinger operator with a PT-symmetric optical potential Bound. Value Probl. (IF 1.7) Pub Date : 2023-10-04 Cemile Nur
We provide estimates for the eigenvalues of non-self-adjoint Sturm–Liouville operators with Dirichlet boundary conditions for a shift of the special potential $4\cos ^{2}x+4iV\sin 2x$ that is a PT-symmetric optical potential, especially when $|c|=|\sqrt{1-4V^{2}}|<2$ or correspondingly $0\leq V<\sqrt {5}/2$ . We obtain some useful equations for calculating Dirichlet eigenvalues also for $|c|\geq 2$
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Analytical mechanics methods in finite element analysis of multibody elastic system Bound. Value Probl. (IF 1.7) Pub Date : 2023-10-04 Maria Luminita Scutaru, Sorin Vlase, Marin Marin
The study of multibody systems with elastic elements involves at the moment the reevaluation of the classical methods of analysis offered by analytical mechanics. Modeling this system with the finite element method requires obtaining the motion equation for an element in the circumstances imposed by a multibody system. The paper aims to present the main analysis methods used by researchers, to make
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Remarks on a fractional nonlinear partial integro-differential equation via the new generalized multivariate Mittag-Leffler function Bound. Value Probl. (IF 1.7) Pub Date : 2023-10-03 Chenkuan Li, Reza Saadati, Joshua Beaudin, Andrii Hrytsenko
Introducing a new generalized multivariate Mittag-Leffler function which is a generalization of the multivariate Mittag-Leffler function, we derive a sufficient condition for the uniqueness of solutions to a brand new boundary value problem of the fractional nonlinear partial integro-differential equation using Banach’s fixed point theorem and Babenko’s technique. This has many potential applications