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Retraction Note: Existence of global solutions for the semilinear nonlocal fractional Cauchy problem of the Schrödinger equation Bound. Value Probl. (IF 1.794) Pub Date : 2021-01-19 Zhen Liu
This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1186/s13661-021-01488-8
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A class of singular diffusion equations based on the convex–nonconvex variation model for noise removal Bound. Value Probl. (IF 1.794) Pub Date : 2021-01-19 Gang Dong; Boying Wu
This paper focuses on the problem of noise removal. First, we propose a new convex–nonconvex variation model for noise removal and consider the nonexistence of solutions of the variation model. Based on the new variation method, we propose a class of singular diffusion equations and prove the of solutions and comparison rule for the new equations. Finally, experimental results illustrate the effectiveness
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Mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions Bound. Value Probl. (IF 1.794) Pub Date : 2021-01-12 Arshad Ali; Kamal Shah; Thabet Abdeljawad; Ibrahim Mahariq; Mostafa Rashdan
The current study is devoted to deriving some results about existence and stability analysis for a nonlinear problem of implicit fractional differential equations (FODEs) with impulsive and integral boundary conditions. The concerned problem involves proportional type delay term. By using Schaefer’s fixed point theorem and Banach’s contraction principle, the required conditions are developed. Also
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Infinitely many homoclinic solutions for sublinear and nonperiodic Schrödinger lattice systems Bound. Value Probl. (IF 1.794) Pub Date : 2021-01-11 Guanwei Chen; Jijiang Sun
By using variational methods we obtain infinitely many nontrivial solutions for a class of nonperiodic Schrödinger lattice systems, where the nonlinearities are sublinear at both zero and infinity.
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Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations Bound. Value Probl. (IF 1.794) Pub Date : 2021-01-09 Liming Xiao; Mingkun Li
In this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics. By the mountain pass theorem we first prove the existence of nonzero weak solution to the static problem, which is the important basis of evolution
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Steady state for a predator–prey cross-diffusion system with the Beddington–DeAngelis and Tanner functional response Bound. Value Probl. (IF 1.794) Pub Date : 2021-01-07 Demou Luo
The main goal of this paper is investigating the existence of nonconstant positive steady states of a linear prey–predator cross-diffusion system with Beddington–DeAngelis and Tanner functional response. An analytical method and fixed point index theory plays a significant role in our main proofs.
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Hopf bifurcation in a delayed reaction–diffusion–advection equation with ideal free dispersal Bound. Value Probl. (IF 1.794) Pub Date : 2021-01-06 Yunfeng Liu; Yuanxian Hui
In this paper, we investigate a delay reaction–diffusion–advection model with ideal free dispersal. The stability of positive steady-state solutions and the existence of the associated Hopf bifurcation are obtained by analyzing the principal eigenvalue of an elliptic operator. By the normal form theory and the center manifold reduction, the stability and bifurcation direction of Hopf bifurcating periodic
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\(L^{\infty }\) decay estimates of solutions of nonlinear parabolic equation Bound. Value Probl. (IF 1.794) Pub Date : 2021-01-04 Hui Wang; Caisheng Chen
In this paper, we are interested in $L^{\infty }$ decay estimates of weak solutions for the doubly nonlinear parabolic equation and the degenerate evolution m-Laplacian equation not in the divergence form. By a modified Moser’s technique we obtain $L^{\infty }$ decay estimates of weak solutiona.
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How far does logistic dampening influence the global solvability of a high-dimensional chemotaxis system? Bound. Value Probl. (IF 1.794) Pub Date : 2021-01-04 Ke Jiang; Yongjie Han
This paper deals with the homogeneous Neumann boundary value problem for chemotaxis system $$\begin{aligned} \textstyle\begin{cases} u_{t} = \Delta u - \nabla \cdot (u\nabla v)+\kappa u-\mu u^{\alpha }, & x\in \Omega, t>0, \\ v_{t} = \Delta v - uv, & x\in \Omega, t>0, \end{cases}\displaystyle \end{aligned}$$ in a smooth bounded domain $\Omega \subset \mathbb{R}^{N}(N\geq 2)$ , where $\alpha >1$ and
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The exterior Dirichlet problems of Monge–Ampère equations in dimension two Bound. Value Probl. (IF 1.794) Pub Date : 2020-12-09 Limei Dai
In this paper, we study the Monge–Ampère equations $\det D^{2}u=f$ in dimension two with f being a perturbation of $f_{0}$ at infinity. First, we obtain the necessary and sufficient conditions for the existence of radial solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a unit ball. Then, using the Perron method, we get the existence of viscosity solutions
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The Pohozaev-type inequalities and their applications for a kind of elliptic equation (system) Bound. Value Probl. (IF 1.794) Pub Date : 2020-12-09 Bingyu Kou; Tianqing An; Zeyan Wang
In this paper, we first derive a new kind of Pohozaev-type inequalities for p-Laplacian equations in a more general class of non-star-shaped domains, and then we take two examples and their graphs to explain the shape of the new kind of the non-star-shaped domain. At last, we extend the results of Pohozaev-type inequalities to elliptic systems, which are used to derive the nonexistence of positive
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A novel method in determining a layered periodic structure Bound. Value Probl. (IF 1.794) Pub Date : 2020-12-09 Yanli Cui; Xiliang Li; Fenglong Qu
This paper is concerned with the inverse scattering of time-harmonic waves by a penetrable structure. By applying the integral equation method, we establish the uniform $L^{p}_{\alpha }\ (1< p\leq 2)$ estimates for the scattered and transmitted wave fields corresponding to a series of incident point sources. Based on these a priori estimates and a mixed reciprocity relation, we prove that the penetrable
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Nonlocal boundary value problems for integro-differential Langevin equation via the generalized Caputo proportional fractional derivative Bound. Value Probl. (IF 1.794) Pub Date : 2020-12-09 Bounmy Khaminsou; Chatthai Thaiprayoon; Jehad Alzabut; Weerawat Sudsutad
Results reported in this paper study the existence and stability of a class of implicit generalized proportional fractional integro-differential Langevin equations with nonlocal fractional integral conditions. The main theorems are proved with the help of Banach’s, Krasnoselskii’s, and Schaefer’s fixed point theorems and Ulam’s approach. Finally, an example is given to demonstrate the applicability
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On global dynamics of 2D convective Cahn–Hilliard equation Bound. Value Probl. (IF 1.794) Pub Date : 2020-12-07 Xiaopeng Zhao
In this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ when the initial value belongs to $H^{1}(\Omega )$ .
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The mixed problem in the theory of strain gradient thermoelasticity approached with the Lagrange identity Bound. Value Probl. (IF 1.794) Pub Date : 2020-12-02 Marin Marin; Sorin Vlase; Ioan Tuns
In our paper we address the thermoelasticity theory of the strain gradient. First, we define the mixed problem with initial and boundary data in this context. Then, with the help of an identity of Lagrange type, we prove some uniqueness theorems with regards to the solution of this problem and two theorems with regards to the continuous dependence of solutions on loads and on initial data. We want
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Global existence and exponential stability of coupled Lamé system with distributed delay and source term without memory term Bound. Value Probl. (IF 1.794) Pub Date : 2020-11-30 Salah Boulaaras; Nadjat Doudi
In this paper, we prove the global existence and exponential energy decay results of a coupled Lamé system with distributed time delay, nonlinear source term, and without memory term by using the Faedo–Galerkin method. In addition, an appropriate Lyapunov functional, more general relaxation functions, and some properties of convex functions are considered.
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General decay and blow-up of solutions for a nonlinear wave equation with memory and fractional boundary damping terms Bound. Value Probl. (IF 1.794) Pub Date : 2020-11-30 Salah Boulaaras; Fares Kamache; Youcef Bouizem; Rafik Guefaifia
The paper studies the global existence and general decay of solutions using Lyapunov functional for a nonlinear wave equation, taking into account the fractional derivative boundary condition and memory term. In addition, we establish the blow-up of solutions with nonpositive initial energy.
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On a new structure of the pantograph inclusion problem in the Caputo conformable setting Bound. Value Probl. (IF 1.794) Pub Date : 2020-11-11 Sabri T. M. Thabet; Sina Etemad; Shahram Rezapour
In this work, we reformulate and investigate the well-known pantograph differential equation by applying newly-defined conformable operators in both Caputo and Riemann–Liouville settings simultaneously for the first time. In fact, we derive the required existence criteria of solutions corresponding to the inclusion version of the three-point Caputo conformable pantograph BVP subject to Riemann–Liouville
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New general decay result for a system of two singular nonlocal viscoelastic equations with general source terms and a wide class of relaxation functions Bound. Value Probl. (IF 1.794) Pub Date : 2020-11-10 Mohammad M. Al-Gharabli; Adel M. Al-Mahdi; Salim A. Messaoudi
This work is concerned with a system of two singular viscoelastic equations with general source terms and nonlocal boundary conditions. We discuss the stabilization of this system under a very general assumption on the behavior of the relaxation function $k_{i}$ , namely, $$\begin{aligned} k_{i}^{\prime }(t)\le -\xi _{i}(t) \Psi _{i} \bigl(k_{i}(t)\bigr),\quad i=1,2. \end{aligned}$$ We establish a
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Construction of invariant solutions and conservation laws to the \((2+1)\)-dimensional integrable coupling of the KdV equation Bound. Value Probl. (IF 1.794) Pub Date : 2020-11-07 Ben Gao; Qinglian Yin
Under investigation in this paper is the $(2+1)$ -dimensional integrable coupling of the KdV equation which has applications in wave propagation on the surface of shallow water. Firstly, based on the Lie symmetry method, infinitesimal generators and an optimal system of the obtained symmetries are presented. At the same time, new analytical exact solutions are computed through the tanh method. In addition
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On resonant mixed Caputo fractional differential equations Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-27 Assia Guezane-Lakoud; Adem Kılıçman
The purpose of this study is to discuss the existence of solutions for a boundary value problem at resonance generated by a nonlinear differential equation involving both right and left Caputo fractional derivatives. The proofs of the existence of solutions are mainly based on Mawhin’s coincidence degree theory. We provide an example to illustrate the main result.
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Resolution and implementation of the nonstationary vorticity velocity pressure formulation of the Navier–Stokes equations Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-23 Mohamed Abdelwahed; Ebtisam Alharbi; Nejmeddine Chorfi; Henda Ouertani
This paper deals with the iterative algorithm and the implementation of the spectral discretization of time-dependent Navier–Stokes equations in dimensions two and three. We present a variational formulation, which includes three independent unknowns: the vorticity, velocity, and pressure. In dimension two, we establish an optimal error estimate for the three unknowns. The discretization is deduced
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Normalized solutions for a coupled fractional Schrödinger system in low dimensions Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-23 Meng Li; Jinchun He; Haoyuan Xu; Meihua Yang
We consider the following coupled fractional Schrödinger system: $$ \textstyle\begin{cases} (-\Delta )^{s}u+\lambda _{1}u=\mu _{1} \vert u \vert ^{2p-2}u+ \beta \vert v \vert ^{p} \vert u \vert ^{p-2}u, \\ (-\Delta )^{s}v+\lambda _{2}v=\mu _{2} \vert v \vert ^{2p-2}v+\beta \vert u \vert ^{p} \vert v \vert ^{p-2}v \end{cases}\displaystyle \quad \text{in } {\mathbb{R}^{N}}, $$ with $0< s<1$ , $2s< N\le
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Well-posedness and behaviors of solutions to an integrable evolution equation Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-22 Sen Ming; Shaoyong Lai; Yeqin Su
This work is devoted to investigating the local well-posedness for an integrable evolution equation and behaviors of its solutions, which possess blow-up criteria and persistence property. The existence and uniqueness of analytic solutions with analytic initial values are established. The solutions are analytic for both variables, globally in space and locally in time. The effects of coefficients λ
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Existence of positive periodic solutions for super-linear neutral Liénard equation with a singularity of attractive type Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-16 Yu Zhu
In this paper, the existence of positive periodic solutions is studied for super-linear neutral Liénard equation with a singularity of attractive type $$ \bigl(x(t)-cx(t-\sigma)\bigr)''+f\bigl(x(t) \bigr)x'(t)-\varphi(t)x^{\mu}(t)+ \frac{\alpha(t)}{x^{\gamma}(t)}=e(t), $$ where $f:(0,+\infty)\rightarrow R$ , $\varphi(t)>0$ and $\alpha(t)>0$ are continuous functions with T-periodicity in the t variable
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Existence of solutions for functional boundary value problems at resonance on the half-line Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-15 Bingzhi Sun; Weihua Jiang
By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ . And an example is given to show that our result here is valid.
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Existence-uniqueness of positive solutions to nonlinear impulsive fractional differential systems and optimal control Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-14 Shu Song; Lingling Zhang; Bibo Zhou; Nan Zhang
In this thesis, we investigate a kind of impulsive fractional order differential systems involving control terms. By using a class of φ-concave-convex mixed monotone operator fixed point theorem, we obtain a theorem on the existence and uniqueness of positive solutions for the impulsive fractional differential equation, and the optimal control problem of positive solutions is also studied. As applications
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An efficient meshless radial point collocation method for nonlinear p-Laplacian equation Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-12 Samaneh Soradi-Zeid; Mehdi Mesrizadeh; Thabet Abdeljawad
This paper considered the spectral meshless radial point interpolation (SMRPI) method to unravel for the nonlinear p-Laplacian equation with mixed Dirichlet and Neumann boundary conditions. Through this assessment, which includes meshless methods and collocation techniques based on radial point interpolation, we construct the shape functions, with the Kronecker delta function property, as basis functions
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Retraction Note: A note on the boundary behavior for a modified Green function in the upper-half space Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-08 Yulian Zhang; Valery Piskarev
This article has been retracted. Please see the retraction notice for more detail: https://doi.org/10.1186/s13661-015-0363-z .
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Multiplicity results for sublinear elliptic equations with sign-changing potential and general nonlinearity Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-07 Wei He; Qingfang Wu
In this paper, we study the following elliptic boundary value problem: $$ \textstyle\begin{cases} -\Delta u+V(x)u=f(x, u),\quad x\in \Omega , \\ u=0, \quad x \in \partial \Omega , \end{cases} $$ where $\Omega \subset {\mathbb {R}}^{N}$ is a bounded domain with smooth boundary ∂Ω, and f is allowed to be sign-changing and is of sublinear growth near infinity in u. For both cases that $V\in L^{N/2}(\Omega
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Low Mach number limit for the compressible Navier–Stokes equations with density-dependent viscosity and vorticity-slip boundary condition Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-07 Dandan Ren; Yunting Ding; Xinfeng Liang
In this paper, we consider the three-dimensional compressible Navier–Stokes equations with density-dependent viscosity and vorticity-slip boundary condition in a bounded smooth domain. The main idea is to derive the uniform estimates for both time and the Mach number. The difficulty is dealing with density-dependent viscosity terms carefully. With the uniform estimates, we can verify the low Mach limit
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Existence of positive solutions for singular Dirichlet boundary value problems with impulse and derivative dependence Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-02 Fengfei Jin; Baoqiang Yan
In this paper, we present a theorem for some impulsive boundary problems with derivative dependence by the upper and lower solutions method. Using the theorem obtained, we consider the existence of positive solutions of some class of singular impulsive boundary problems.
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The applications of Sobolev inequalities in proving the existence of solution of the quasilinear parabolic equation Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-01 Yuanfei Li; Lianhong Guo; Peng Zeng
The aim of this paper is to show some applications of Sobolev inequalities in partial differential equations. With the aid of some well-known inequalities, we derive the existence of global solution for the quasilinear parabolic equations. When the blow-up occurs, we derive the lower bound of the blow-up solution.
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Existence results for first derivative dependent ϕ-Laplacian boundary value problems Bound. Value Probl. (IF 1.794) Pub Date : 2020-10-01 Imran Talib; Thabet Abdeljawad
Our main concern in this article is to investigate the existence of solution for the boundary-value problem $$\begin{aligned}& (\phi \bigl(x'(t)\bigr)'=g_{1} \bigl(t,x(t),x'(t)\bigr),\quad \forall t\in [0,1], \\& \Upsilon _{1}\bigl(x(0),x(1),x'(0)\bigr)=0, \\& \Upsilon _{2}\bigl(x(0),x(1),x'(1)\bigr)=0, \end{aligned}$$ where $g_{1}:[0,1]\times \mathbb{R}^{2}\rightarrow \mathbb{R}$ is an $L^{1}$ -Carathéodory
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On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses Bound. Value Probl. (IF 1.794) Pub Date : 2020-09-25 Bo Zhu; Baoyan Han; Lishan Liu; Wenguang Yu
In this paper, we consider the initial boundary value problem for a class of nonlinear fractional partial integro-differential equations of mixed type with non-instantaneous impulses in Banach spaces. Sufficient conditions of existence and uniqueness of PC-mild solutions for the equations are obtained via general Banach contraction mapping principle, Krasnoselskii’s fixed point theorem, and α-order
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Nonlinear nonhomogeneous Dirichlet problems with singular and convection terms Bound. Value Probl. (IF 1.794) Pub Date : 2020-09-23 Nikolaos S. Papageorgiou; Youpei Zhang
We consider a nonlinear Dirichlet problem driven by a general nonhomogeneous differential operator and with a reaction exhibiting the combined effects of a parametric singular term plus a Carathéodory perturbation $f(z,x,y)$ which is only locally defined in $x \in {\mathbb {R}} $ . Using the frozen variable method, we prove the existence of a positive smooth solution, when the parameter is small.
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Spectral discretization of time-dependent vorticity–velocity–pressure formulation of the Navier–Stokes equations Bound. Value Probl. (IF 1.794) Pub Date : 2020-09-18 Mohamed Abdelwahed; Nejmeddine Chorfi
In this work, we propose a nonstationary Navier–Stokes problem equipped with an unusual boundary condition. The time discretization of such a problem is based on the backward Euler’s scheme. However, the variational formulation deduced from the nonstationary Navier–Stokes equations is discretized using the spectral method. We prove that the time semidiscrete problem and the full spectral discrete one
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Blow-up criterion for the density dependent inviscid Boussinesq equations Bound. Value Probl. (IF 1.794) Pub Date : 2020-09-18 Li Li; Yanping Zhou
In this work, we consider the density-dependent incompressible inviscid Boussinesq equations in $\mathbb{R}^{N}\ (N\geq 2)$ . By using the basic energy method, we first give the a priori estimates of smooth solutions and then get a blow-up criterion. This shows that the maximum norm of the gradient velocity field controls the breakdown of smooth solutions of the density-dependent inviscid Boussinesq
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Multiplicity of solutions for a class of fractional \(p(x,\cdot )\)-Kirchhoff-type problems without the Ambrosetti–Rabinowitz condition Bound. Value Probl. (IF 1.794) Pub Date : 2020-09-15 M. K. Hamdani; J. Zuo; N. T. Chung; D. D. Repovš
We are interested in the existence of solutions for the following fractional $p(x,\cdot )$ -Kirchhoff-type problem: $$ \textstyle\begin{cases} M ( \int _{\Omega \times \Omega } {\frac{ \vert u(x)-u(y) \vert ^{p(x,y)}}{p(x,y) \vert x-y \vert ^{N+p(x,y)s}}} \,dx \,dy )(-\Delta )^{s}_{p(x,\cdot )}u = f(x,u), \quad x\in \Omega , \\ u= 0, \quad x\in \partial \Omega , \end{cases} $$ where $\Omega \subset
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Existence of a mountain pass solution for a nonlocal fractional \((p, q)\)-Laplacian problem Bound. Value Probl. (IF 1.794) Pub Date : 2020-09-09 F. Behboudi; A. Razani; M. Oveisiha
Here, a nonlocal nonlinear operator known as the fractional $(p,q)$ -Laplacian is considered. The existence of a mountain pass solution is proved via critical point theory and variational methods. To this aim, the well-known theorem on the construction of the critical set of functionals with a weak compactness condition is applied.
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Ground states for infinite lattices with nearest neighbor interaction Bound. Value Probl. (IF 1.794) Pub Date : 2020-09-09 Peng Chen; Die Hu; Yuanyuan Zhang
Sun and Ma (J. Differ. Equ. 255:2534–2563, 2013) proved the existence of a nonzero T-periodic solution for a class of one-dimensional lattice dynamical systems, $$\begin{aligned} \ddot{q_{i}}=\varPhi _{i-1}'(q_{i-1}-q_{i})- \varPhi _{i}'(q_{i}-q_{i+1}),\quad i\in \mathbb{Z}, \end{aligned}$$ where $q_{i}$ denotes the co-ordinate of the ith particle and $\varPhi _{i}$ denotes the potential of the interaction
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Higher integrability for obstacle problem related to the singular porous medium equation Bound. Value Probl. (IF 1.794) Pub Date : 2020-09-07 Qifan Li
In this paper we study the self-improving property of the obstacle problem related to the singular porous medium equation by using the method developed by Gianazza and Schwarzacher (J. Funct. Anal. 277(12):1–57, 2019). We establish a local higher integrability result for the spatial gradient of the mth power of nonnegative weak solutions, under some suitable regularity assumptions on the obstacle function
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On locally superquadratic Hamiltonian systems with periodic potential Bound. Value Probl. (IF 1.794) Pub Date : 2020-09-01 Yiwei Ye
In this paper, we study the second-order Hamiltonian systems $$ \ddot{u}-L(t)u+\nabla W(t,u)=0, $$ where $t\in \mathbb{R}$ , $u\in \mathbb{R}^{N}$ , L and W depend periodically on t, 0 lies in a spectral gap of the operator $-d^{2}/dt^{2}+L(t)$ and $W(t,x)$ is locally superquadratic. Replacing the common superquadratic condition that $\lim_{|x|\rightarrow \infty }\frac{W(t,x)}{|x|^{2}}=+\infty $ uniformly
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Concentrated solutions for a critical nonlocal problem Bound. Value Probl. (IF 1.794) Pub Date : 2020-09-01 Qingfang Wang
In this paper, we deal with a class of fractional critical problems. Under some suitable assumptions, we derive the existence of a positive solution concentrating at the critical point of the Robin function by using the Lyapunov–Schmidt reduction method. Comparing with previous work, we encounter some new challenges because of a nonlocal term. By making some delicate estimates for the nonlocal term
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The existence of nontrivial solution of a class of Schrödinger–Bopp–Podolsky system with critical growth Bound. Value Probl. (IF 1.794) Pub Date : 2020-08-28 Jie Yang; Haibo Chen; Senli Liu
We consider the following Schrödinger–Bopp–Podolsky problem: $$ \textstyle\begin{cases} -\Delta u+V(x) u+\phi u=\lambda f(u)+ \vert u \vert ^{4}u,& \text{in } \mathbb{R}^{3}, \\ -\Delta \phi +\Delta ^{2}\phi = u^{2}, & \text{in } \mathbb{R}^{3}. \end{cases} $$ We prove the existence result without any growth and Ambrosetti–Rabinowitz conditions. In the proofs, we apply a cut-off function, the mountain
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Weak and strong singularities problems to Liénard equation Bound. Value Probl. (IF 1.794) Pub Date : 2020-08-28 Yun Xin; Guixin Hu
This paper is devoted to an investigation of the existence of a positive periodic solution for the following singular Liénard equation: $$ x''+f\bigl(x(t)\bigr)x'(t)+a(t)x= \frac{b(t)}{x^{\alpha }}+e(t), $$ where the external force $e(t)$ may change sign, α is a constant and $\alpha >0$ . The novelty of the present article is that for the first time we show that weak and strong singularities enables
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Infinitely many positive solutions for a double phase problem Bound. Value Probl. (IF 1.794) Pub Date : 2020-08-28 Bei-Lei Zhang; Bin Ge; Gang-Ling Hou
This paper is concerned with the existence of infinitely many positive solutions to a class of double phase problem. By variational methods and the theory of the Musielak–Orlicz–Sobolev space, we establish the existence of infinitely many positive solutions whose $W_{0}^{1,H}(\varOmega )$ -norms and $L^{\infty }$ -norms tend to zero under suitable hypotheses about nonlinearity.
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On decay and blow-up of solutions for a nonlinear Petrovsky system with conical degeneration Bound. Value Probl. (IF 1.794) Pub Date : 2020-08-20 Jiali Yu; Yadong Shang; Huafei Di
This paper deals with a class of Petrovsky system with nonlinear damping $$\begin{aligned} w_{tt}+\Delta _{\mathbb{B}}^{2}w-k_{2} \Delta _{\mathbb{B}}w_{t}+aw_{t} \vert w_{t} \vert ^{m-2}=bw \vert w \vert ^{p-2} \end{aligned}$$ on a manifold with conical singularity, where $\Delta _{\mathbb{B}}$ is a Fuchsian-type Laplace operator with totally characteristic degeneracy on the boundary $x_{1}=0$ . We
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Existence of solutions for tripled system of fractional differential equations involving cyclic permutation boundary conditions Bound. Value Probl. (IF 1.794) Pub Date : 2020-08-18 Mohammed M. Matar; Iman Abo Amra; Jehad Alzabut
In this paper, we introduce and study a tripled system of three associated fractional differential equations. Prior to proceeding to the main results, the proposed system is converted into an equivalent integral form by the help of fractional calculus. Our approach is based on using the addressed tripled system with cyclic permutation boundary conditions. The existence and uniqueness of solutions are
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Boundary shape function method for nonlinear BVP, automatically satisfying prescribed multipoint boundary conditions Bound. Value Probl. (IF 1.794) Pub Date : 2020-08-14 Chein-Shan Liu; Chih-Wen Chang
It is difficult to exactly and automatically satisfy nonseparable multipoint boundary conditions by numerical methods. With this in mind, we develop a novel algorithm to find solution for a second-order nonlinear boundary value problem (BVP), which automatically satisfies the multipoint boundary conditions prescribed. A novel concept of boundary shape function (BSF) is introduced, whose existence is
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Qualitative analysis of nonlinear coupled pantograph differential equations of fractional order with integral boundary conditions Bound. Value Probl. (IF 1.794) Pub Date : 2020-08-12 Hussam Alrabaiah; Israr Ahmad; Kamal Shah; Ghaus Ur Rahman
In this research article, we develop a qualitative analysis to a class of nonlinear coupled system of fractional delay differential equations (FDDEs). Under the integral boundary conditions, existence and uniqueness for the solution of this system are carried out. With the help of Leray–Schauder and Banach fixed point theorem, we establish indispensable results. Also, some results affiliated to Ulam–Hyers
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Well-posedness of the solution of the fractional semilinear pseudo-parabolic equation Bound. Value Probl. (IF 1.794) Pub Date : 2020-08-12 Jiazhuo Cheng; Shaomei Fang
This article concerns the Cauchy problem for the fractional semilinear pseudo-parabolic equation. Through the Green’s function method, we prove the pointwise convergence rate of the solution. Furthermore, using this precise pointwise structure, we introduce a Sobolev space condition with negative index on the initial data and give the nonlinear critical index for blowing up.
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On the numerical solutions of two-dimensional scattering problems for an open arc Bound. Value Probl. (IF 1.794) Pub Date : 2020-08-06 Hu Li; Jin Huang; Guang Zeng
For the scattering problems of acoustic wave for an open arc in two dimensions, we give a uniqueness and existence analysis via the single layer potential approach leading to a system of integral equations that contains a weakly singular operator. For its numerical solutions, we describe an $O(h^{3})$ order quadrature method based on the specific integral formula including convergence and stability
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On a system of fractional q-differential inclusions via sum of two multi-term functions on a time scale Bound. Value Probl. (IF 1.794) Pub Date : 2020-08-06 Mohammad Esmael Samei; Shahram Rezapour
Nowadays most researchers have been focused on fractional calculus because it has been proved that fractional derivatives could describe most phenomena better than usual derivations. Numerical parts of fractional calculus such as q-derivations are considered by researchers. In this work, our aim is to review the existence of solution for an m-dimensional system of fractional q-differential inclusions
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Existence result for a Kirchhoff elliptic system with variable parameters and additive right-hand side via sub- and supersolution method Bound. Value Probl. (IF 1.794) Pub Date : 2020-08-05 Mohamed Haiour; Salah Boulaaras; Youcef Bouizem; Rafik Guefaifia
The paper deals with the study of the existence result for a Kirchhoff elliptic system with additive right-hand side and variable parameters by using the sub-/supersolution method. Our study is a natural extension result of our previous one in (Boulaaras and Guefaifia in Math. Methods Appl. Sci. 41:5203–5210, 2018), where we discussed only the simple case when the parameters are constant.
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Ground state and nodal solutions for critical Kirchhoff–Schrödinger–Poisson systems with an asymptotically 3-linear growth nonlinearity Bound. Value Probl. (IF 1.794) Pub Date : 2020-08-04 Chungen Liu; Hua-Bo Zhang
In this paper, we consider the existence of a least energy nodal solution and a ground state solution, energy doubling property and asymptotic behavior of solutions of the following critical problem: $$ \textstyle\begin{cases} -(a+ b\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}\,dx)\Delta u+V(x)u+\lambda \phi u= \vert u \vert ^{4}u+ k f(u),&x\in \mathbb{R}^{3}, \\ -\Delta \phi =u^{2},&x\in \mathbb{R}^{3}
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Hopf bifurcation analysis of nonlinear HIV infection model and the effect of delayed immune response with drug therapies Bound. Value Probl. (IF 1.794) Pub Date : 2020-08-03 V. Geetha; S. Balamuralitharan
A mathematical model of HIV infection with the combination of drug therapy including cytotoxic T-lymphocyte (CTL) and the antibody immune response is examined. The threshold value represented as the basic reproduction ratio $R_{0}$ is derived. This reveals that $R_{0} < 1$ is locally asymptotically stable in the viral free steady state, and the infected steady state condition remains locally asymptotically
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On the existence of three solutions of Dirichlet fractional systems involving the p-Laplacian with Lipschitz nonlinearity Bound. Value Probl. (IF 1.794) Pub Date : 2020-07-31 Rafik Guefaifia; Salah Boulaaras; Fares Kamache
A class of perturbed fractional nonlinear systems is studied. The dynamical system possesses two control parameters and a Lipschitz nonlinearity order of $p-1$ . The multiplicity of the weak solutions is proved by means of the variational method and by Ricceri critical points theorems. An illustrative example is analyzed in order to highlight the obtained result.
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Existence and multiplicity of solutions for nonlocal fourth-order elliptic equations with combined nonlinearities Bound. Value Probl. (IF 1.794) Pub Date : 2020-07-31 Ru Yuanfang; An Yukun
This paper is concerned with the following nonlocal fourth-order elliptic problem: $$\begin{aligned} \textstyle\begin{cases} \Delta ^{2}u-m(\int _{\varOmega } \vert \nabla u \vert ^{2} \,dx)\Delta u=a(x) \vert u \vert ^{s-2}u+f(x,u), \quad x\in \varOmega , \\ u=\Delta u=0,\quad x\in \partial \varOmega , \end{cases}\displaystyle \end{aligned}$$ by using the mountain pass theorem, the least action principle
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A note on singular two-dimensional fractional coupled Burgers’ equation and triple Laplace Adomian decomposition method Bound. Value Probl. (IF 1.794) Pub Date : 2020-07-23 Hassan Eltayeb; Imed Bachar
The present article focuses on how to find the exact solutions of the time-fractional regular and singular coupled Burgers’ equations by applying a new method that is called triple Laplace and Adomian decomposition method. Furthermore, the proposed method is a strong tool for solving many problems. The accuracy of the method is considered through the use of some examples, and the results obtained are
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