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Existence and multiplicity of nontrivial solutions for a semilinear biharmonic equation with weight functions Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210623
Xiyou Cheng, Zhaosheng Feng, Lei WeiWe consider the existence and multiplicity of nontrivial solutions for a semilinear biharmonic equation with the concaveconvex nonlinearities $ f(x) u^{q1} u $ and $ h(x) u^{p1} u $ under certain conditions on $ f(x), \, h(x) $, $ p $ and $ q $. Applying the Nehari manifold method along with the fibering maps and the minimization method, we study the effect of $ f(x) $ and $ h(x) $ on the existence

Symmetry of positive solutions for systems of fractional Hartree equations Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210623
Yan Deng, Junfang Zhao, Baozeng ChuIn this paper, we deal with a system of fractional Hartree equations. By means of a direct method of moving planes, the radial symmetry and monotonicity of positive solutions are presented.

Uniform polynomial stability of second order integrodifferential equations in Hilbert spaces with positive definite kernels Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210623
KunPeng Jin, Jin Liang, TiJun XiaoWe are concerned with the polynomial stability and the integrability of the energy for second order integrodifferential equations in Hilbert spaces with positive definite kernels, where the memory can be oscillating or signvarying or not locally absolutely continuous (without any control conditions on the derivative of the kernel). For this stability problem, tools from the theory of existing positive

$ W^{2, p} $regularity for asymptotically regular fully nonlinear elliptic and parabolic equations with oblique boundary values Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210623
Junjie Zhang, Shenzhou Zheng, Chunyan ZuoWe prove a global $ W^{2, p} $estimate for the viscosity solution to fully nonlinear elliptic equations $ F(x, u, Du, D^{2}u) = f(x) $ with oblique boundary condition in a bounded $ C^{2, \alpha} $domain for every $ \alpha\in (0, 1) $. Here, the nonlinearities $ F $ is assumed to be asymptotically $ \delta $regular to an operator $ G $ that is $ (\delta, R) $vanishing with respect to $ x $. We

Nonautonomous weakly damped plate model on timedependent domains Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210623
Penghui Zhang, Zhaosheng Feng, Lu YangWe are concerned with dynamics of the weakly damped plate equation on a timedependent domain. Under the assumption that the domain is timelike and expanding, we obtain the existence of timedependent attractors, where the nonlinear term has a critical growth.

Nonstandard boundary conditions for the linearized Kortewegde Vries equation Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210609
Mostafa Abounouh, Hassan AlMoatassime, Sabah KaouriThis paper aims to solve numerically the linearized Kortewegde Vries equation. We begin by deriving suitable boundary conditions then approximate them using finite difference method. The methodology of derivation, used in this paper, yields to NonStandard Boundary Conditions (NSBC) that perfectly absorb wave reflections at the boundary. In addition, these NSBC are exact and local in time and space

Diffusionapproximation for a kinetic spraylike system with random forcing Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210422
Arnaud Debussche, Angelo Rosello, Julien VovelleWe study a kinetic toy model for a spray of particles immersed in an ambient fluid, subject to some additional random forcing given by a mixing, spacedependent Markov process. Using the perturbed test function method, we derive the hydrodynamic limit of the kinetic system. The law of the limiting density satisfies a stochastic conservation equation in Stratonovich form, whose drift and diffusion coefficients

Largetime existence for onedimensional GreenNaghdi equations with vorticity Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210422
Colette Guillopé, Samer Israwi, Raafat TalhoukThis essay is concerned with the onedimensional GreenNaghdi equations in the presence of a nonzero vorticity according to the derivation in [5], and with the addition of a small surface tension. The GreenNaghdi system is first rewritten as an equivalent system by using an adequate change of unknowns. We show that solutions to this model may be obtained by a standard Picard iterative scheme. No

Discrete approximation of dynamic phasefield fracture in viscoelastic materials Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210621
Marita Thomas, Sven TornquistThis contribution deals with the analysis of models for phasefield fracture in viscoelastic materials with dynamic effects. The evolution of damage is handled in two different ways: As a viscous evolution with a quadratic dissipation potential and as a rateindependent law with a positively $ 1 $homogeneous dissipation potential. Both evolution laws encode a nonsmooth constraint that ensures the

Fractional and fractal advectiondispersion model Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210518
Amy Allwright, Abdon Atangana, Toufik MekkaouiA fractal advectiondispersion equation and a fractional spacetime advectiondispersion equation have been developed to improve the simulation of groundwater transport in fractured aquifers. The spacetime fractional advectiondispersion simulation is limited due to complex algorithms and the computational power required; conversely, the fractal advectiondispersion equation can be solved simply,

An analysis of tuberculosis model with exponential decay law operator Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210519
Ebenezer Bonyah, FatmawatiIn this paper, we explore the dynamics of tuberculosis (TB) epidemic model that includes the recruitment rate in both susceptible and infected population. Stability and sensitivity analysis of the classical TB model is carried out. CaputoFabrizio (CF) operator is then used to explain the dynamics of the TB model. The concept of fixed point theory is employed to obtain the existence and uniqueness

More new results on integral inequalities for generalized \begin{document}$ \mathcal{K} $\end{document}fractional conformable Integral operators Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210518
YuMing Chu, Saima Rashid, Fahd Jarad, Muhammad Aslam Noor, Humaira KalsoomThis paper aims to investigate the several generalizations by newly proposed generalized $ \mathcal{K} $fractional conformable integral operator. Based on these novel ideas, we derived a novel framework to study for $ \breve{C} $eby$ \breve{s} $ev and P$ \acute{o} $lyaSzeg$ \ddot{o} $ type inequalities by generalized $ \mathcal{K} $fractional conformable integral operator. Several special cases

Bounded perturbation for evolution equations with a parameter & application to population dynamics Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210514
Emile Franc Doungmo GoufoEvolution equations using derivatives of fractional order like Caputo's derivative or RiemannLiouville's derivative have been intensively analyzed in numerous works. But the classical bounded perturbation theorem has been proven not to be in general true for these models, especially for solution operators of evolution equations with fractional order derivative $ \alpha $ less than $ 1 $ ($ 0<\alpha<1

Application of aggregation of variables methods to a class of twotime reactiondiffusionchemotaxis models of spatially structured populations with constant diffusion Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210519
Anouar El Harrak, Amal Bergam, Tri NguyenHuu, Pierre Auger, Rachid MchichThe main goal of this paper is to adapt a class of complexity reduction methods called aggregation of variables methods to the construction of reduced models of twotime reactiondiffusionchemotaxis models of spatially structured populations and to provide an error bound of the approximate dynamics. Aggregation of variables methods are general techniques that allow reducing the dimension of a mathematical

A posteriori error estimates for a finite volume scheme applied to a nonlinear reactiondiffusion equation in population dynamics Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210518
Anouar El Harrak, Hatim Tayeq, Amal BergamThis work gives a posteriori error estimates for a finite volume implicit scheme, applied to a twotime nonlinear reactiondiffusion problem in population dynamics, whose evolution processes occur at two different time scales, represented by a parameter $ \varepsilon>0 $ small enough. This work consists of building error indicators concerning time and space approximations and using them as a tool of

System response of an alcoholism model under the effect of immigration via nonsingular kernel derivative Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210514
Fırat Evirgen, Sümeyra Uçar, Necati Özdemir, Zakia HammouchIn this study, we aim to comprehensively investigate a drinking model connected to immigration in terms of AtanganaBaleanu derivative in Caputo type. To do this, we firstly extend the model describing drinking model by changing the derivative with time fractional derivative having MittagLeffler kernel. The existence and uniqueness of the drinking model solutions together with the stability analysis

Dynamical behaviors and oblique resonant nonlinear waves with dualpower law nonlinearity and conformable temporal evolution Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210514
Md. Golam Hafez, Sayed Allamah Iqbal, Asaduzzaman, Zakia HammouchIn this article, the oblique resonant traveling waves and dynamical behaviors of (2+1)dimensional Nonlinear Schrödinger equation along with dualpower law nonlinearity, and fractal conformable temporal evolution are reported. The considered equation is converted to an ordinary differential equation by taking the traveling variable wave transform and properties of Khalil's conformable derivative into

New class of volterra integrodifferential equations with fractalfractional operators: Existence, uniqueness and numerical scheme Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210518
Seda İğret ArazIn this paper, we introduce a new fractional integrodifferential equation involving newly introduced differential and integral operators socalled fractalfractional derivatives and integrals. We present a numerical scheme that is convenient for obtaining solution of such equations. We give the general conditions for the existence and uniqueness of the solution of the considered equation using Banach

Lyapunov type inequality in the frame of generalized Caputo derivatives Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210514
Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad, Saed F. Mallak, Hussam AlrabaiahIn this paper, we establish the Lyapunovtype inequality for boundary value problems involving generalized Caputo fractional derivatives that unite the Caputo and CaputoHadamrad fractional derivatives. An application about the zeros of generalized types of MittagLeffler functions is given.

Fractional AdamsBashforth scheme with the LiouvilleCaputo derivative and application to chaotic systems Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210514
Kolade M. Owolabi, Abdon Atangana, Jose Francisco GómezAguilarA recently proposed numerical scheme for solving nonlinear ordinary differential equations with integer and noninteger LiouvilleCaputo derivative is applied to three systems with chaotic solutions. The AdamsBashforth scheme involving Lagrange interpolation and the fundamental theorem of fractional calculus. We provide the existence and uniqueness of solutions, also the convergence result is stated

Finite element method for twodimensional linear advection equations based on spline method Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210519
Kai Qu, Qi Dong, Chanjie Li, Feiyu ZhangA new method for some advection equations is derived and analyzed, where the finite element method is constructed by using spline. A proper spline subspace is discussed for satisfying boundary conditions. Meanwhile, in order to get more accuracy solutions, spline method is connected with finite element method. Furthermore, the stability and convergence are discussed rigorously. Two numerical experiments

Marangoni forced convective Casson type nanofluid flow in the presence of Lorentz force generated by Riga plate Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210514
Ghulam Rasool, Anum Shafiq, Chaudry Masood KhaliqueThe present communication aims to investigate Marangoni based convective Casson modeled nanofluid flow influenced by the presence of Lorentz forces instigated into the model by an aligned array of magnets in the form of Riga pattern. The exponentially decaying Lorentz force is considered using the Grinberg term. On the liquid  gas or liquid  liquid interface, a realistic temperature and concentration

Optimal control strategy for an agestructured SIR endemic model Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210519
Hassan Tahir, Asaf Khan, Anwarud Din, Amir Khan, Gul ZamanIn this article, we consider an agestructured SIR endemic model. The model is formulated from the available literature while adding some new assumptions. In order to control the infection, we consider vaccination as a control variable and a control problem is presented for further analysis. The method of weak derivatives and minimizing sequence argument are used for deriving necessary conditions and

Existence and uniqueness results for a smoking model with determination and education in the frame of nonsingular derivatives Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210514
Sümeyra UçarThese days, it is widely known that smoking causes numerous diseases, as well as resulting in many avoidable losses of life globally, and therefore encumbers the society with enormous unnecessary burdens. The aim of this study is to examine indepth a smoking model that is mainly influenced by determination and educational actions via CF and AB derivatives. For both fractional order models, the fixed

Novel comparison of numerical and analytical methods for fractional Burger–Fisher equation Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210514
Asif Yokus, Mehmet YavuzIn this paper, we investigate some analytical, numerical and approximate analytical methods by considering timefractional nonlinear Burger–Fisher equation (FBFE). (1/G$ ' $)expansion method, finite difference method (FDM) and Laplace perturbation method (LPM) are considered to solve the FBFE. Firstly, we obtain the analytical solution of the mentioned problem via (1/G$ ' $)expansion method. Also

Multibubble nodal solutions to slightly subcritical elliptic problems with Hardy terms in symmetric domains Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210518
Thomas Bartsch, Qianqiao GuoWe consider the slightly subcritical elliptic problem with Hardy term $ \left\{ \begin{aligned}  \Delta u\mu\frac{u}{x^2} & = u^{2^{\ast}2 \varepsilon}u &&\quad \rm{in } \Omega\subset{\mathbb{R}}^N, \\\ u & = 0&&\quad \rm{on } \partial \Omega, \end{aligned} \right. $

Bound states for fractional SchrödingerPoisson system with critical exponent Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210324
Mengyao Chen, Qi Li, Shuangjie PengThis paper deals with the fractional SchrödingerPoisson system $ \begin{equation*} \left\{ \begin{array}{ll} \varepsilon^{2s}(\Delta )^su+V(x)u+K(x)\phi u = u^{2_{s}^{*}2}u, & \text{in}\ {\Bbb R}^3,\\ (\Delta)^{t}\phi = K(x)u^2, & \text{in}\ {\Bbb R}^3, \end{array} \right. \end{equation*} $

Ground state for fractional SchrödingerPoisson equation in CoulombSobolev space Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210518
Hangzhou Hu, Yuan Li, Dun ZhaoWe consider the following fractional SchrödingerPoisson equation with combined nonlinearities $ \begin{equation*} \begin{cases} (\Delta)^su+\phi u = u^{s^*2}u+\muu^{p2}u \,\,\,\rm{in}\ \mathbb{R}^3,\\ \Delta \phi = 4\pi u^2\ \rm{in}\ \mathbb{R}^3, \end{cases} \end{equation*} $

The OrliczMinkowski problem for polytopes Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210424
Meiyue Jiang, Chu WangThe OrliczMinkowski problem for polytopes is studied, and some existence results are established by the variational method.

The Orlicz Minkowski problem involving $ 0 < p < 1 $: From one constant to an infinite interval Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210324
Yuxin Tan, Yijing SunIn this paper we study the existence of convex bodies for the Orlicz Minkowski problem $ c\varphi (h_{K})dS(K, \cdot) = d\mu\quad \mbox{on}\, {\mathbb{S}}^{n1} $

Positive least energy solutions for kcoupled critical systems involving fractional Laplacian Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210422
Xin Yin, Wenming ZouIn this paper, we study the following $ k $

Cahn–Hilliard–Brinkman systems for tumour growth Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210324
Matthias Ebenbeck, Harald Garcke, Robert NürnbergA phase field model for tumour growth is introduced that is based on a Brinkman law for convective velocity fields. The model couples a convective Cahn–Hilliard equation for the evolution of the tumour to a reactiondiffusionadvection equation for a nutrient and to a Brinkman–Stokes type law for the fluid velocity. The model is derived from basic thermodynamical principles, sharp interface limits

Single point blowup and final profile for a perturbed nonlinear heat equation with a gradient and a nonlocal term Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210324
Bouthaina Abdelhedi, Hatem ZaagWe consider in this paper a perturbation of the standard semilinear heat equation by a term involving the space derivative and a nonlocal term. In some earlier work [1], we constructed a blowup solution for that equation, and showed that it blows up (at least) at the origin. We also derived the so called "intermediate blowup profile". In this paper, we prove the single point blowup property and

A hyperbolicellipticparabolic PDE model describing chemotactic E. Coli colonies Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210324
Danielle Hilhorst, Pierre RouxWe study a modified version of an initialboundary value problem describing the formation of colony patterns of bacteria Escherichia Coli. The original system of three parabolic equations was studied numerically and analytically and gave insights into the underlying mechanisms of chemotaxis. We focus here on the parabolicellipticparabolic approximation and the hyperbolicellipticparabolic limiting

Global attractor for a nonlinear Schrödinger equation with a nonlinearity concentrated in one point Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210324
Wided KechicheWe consider the nonlinear Schrödinger equation in dimension one with a nonlinearity concentrated in one point. We prove that this equation provides an infinite dimensional dynamical system. We also study the asymptotic behavior of the dynamics. We prove the existence of a global attractor for the system.

Mathematical modelling of cytosolic calcium concentration distribution using nonlocal fractional operator Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210303
Ritu Agarwal, Kritika, Sunil Dutt Purohit, Devendra KumarThe aim of this paper is to study the calcium profile governed by the advection diffusion equation. The mathematical and computational modeling has provided insights to understand the calcium signalling which depends upon cytosolic calcium concentration. Here the model includes the important physiological parameters like diffusion coefficient, flow velocity etc. The mathematical model is fractionalised

Computational and numerical simulations for the deoxyribonucleic acid (DNA) model Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210303
Raghda A. M. Attia, Dumitru Baleanu, Dianchen Lu, Mostafa M. A. Khater, ElSayed AhmedIn this research paper, the modified Khater method, the Adomian decomposition method, and Bspline techniques (cubic, quintic, and septic) are applied to the deoxyribonucleic acid (DNA) model to get the analytical, semianalytical, and numerical solutions. These solutions comprise much information about the dynamical behavior of the homogenous long elastic rods with a circular section. These rods constitute

Analytical study of fractional nonlinear Schrödinger equation with harmonic oscillator Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210303
Amit Goswami, Sushila Rathore, Jagdev Singh, Devendra KumarIn this paper, an effective analytical scheme based on Sumudu transform known as homotopy perturbation Sumudu transform method (HPSTM) is employed to find numerical solutions of time fractional Schrödinger equations with harmonic oscillator.These nonlinear time fractional Schrödinger equations describe the various phenomena in physics such as motion of quantum oscillator, lattice vibration, propagation

Asymptotic behaviors of solution to partial differential equation with Caputo–Hadamard derivative and fractional Laplacian: Hyperbolic case Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210303
Changpin Li, Zhiqiang LiThis paper is concerned with the asymptotic behaviors of solution to time–space fractional partial differential equation with Caputo–Hadamard derivative (in time) and fractional Laplacian (in space) in the hyperbolic case, that is, the Caputo–Hadamard derivative order $ \alpha $ lies in $ 1<\alpha<2 $. In view of the technique of integral transforms, the fundamental solutions and the exact solution

Some new bounds analogous to generalized proportional fractional integral operator with respect to another function Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210303
Saima Rashid, Fahd Jarad, Zakia HammouchThe present article deals with the new estimates in the view of generalized proportional fractional integral with respect to another function. In the present investigation, we focus on driving certain new classes of integral inequalities utilizing a family of positive functions $ n(n\in\mathbb{N}) $ for this newly defined operator. From the computed outcomes, we concluded some new variants for classical

A robust computational framework for analyzing fractional dynamical systems Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210303
Khosro Sayevand, Valeyollah MoradiThis study outlines a modiﬁed implicit ﬁnite difference method for approximating the local stable manifold near a hyperbolic equilibrium point for a nonlinear systems of fractional differential equations. The fractional derivative is described in the Caputo sense of order $ \alpha\; (0<\alpha \le1) $ which is approximated based on the modified trapezoidal quadrature rule of order $ O(\triangle t ^{2\alpha})

Class of integrals and applications of fractional kinetic equation with the generalized multiindex Bessel function Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210303
Dayalal Suthar, Sunil Dutt Purohit, Haile Habenom, Jagdev SinghIn this article, we have investigated certain definite integrals and various integral transforms of the generalized multiindex Bessel function, such as Euler transform, Laplace transform, Whittaker transform, Ktransform and Fourier transforms. Also found the applications of the problem on fractional kinetic equation pertaining to the generalized multiindex Bessel function using the Sumudu transform

Traveling wave fronts in a diffusive and competitive LotkaVolterra system Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210129
Zengji Du, Shuling Yan, Kaige ZhuangIn this paper, we consider a twospecies competitive and diffusive system with nonlocal delays. We investigate the existence of traveling wave fronts of the system by employing linear chain techniques and geometric singular perturbation theory. The existence of the traveling wave fronts analogous to a bistable wavefront for a single species is proved by transforming the system with nonlocal delays

Existence of nontrivial solutions to ChernSimonsSchrödinger system with indefinite potential Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210129
Jincai Kang, Chunlei TangWe consider a class of ChernSimonsSchrödinger system $ \begin{align*} \begin{cases} \Delta u+V(x) u+A_{0}u+\sum\limits_{j = 1}^{2} A_{j}^{2}u = g(u), \\ \partial_{1}A_{0} = A_{2}u^{2}, \ \ \partial_{2}A_{0} = A_{1}u^{2}, \\ \partial_{1}A_{2}\partial_{2}A_{1} = \frac{1}{2}u^{2}, \ \ \partial_{1}A_{1}+\partial_{2}A_{2} = 0, \end{cases} \end{align*} $

Equilibrium of immersed hyperelastic solids Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210114
Manuel Friedrich, Martin Kružík, Ulisse StefanelliWe discuss different equilibrium problems for hyperelastic solids immersed in a fluid at rest. In particular, solids are subjected to gravity and hydrostatic pressure on their immersed boundaries. By means of a variational approach, we discuss freefloating bodies, anchored solids, and floating vessels. Conditions for the existence of local and global energy minimizers are presented.

Damping, stabilization, and numerical filtering for the modeling and the simulation of time dependent PDEs Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210114
JeanPaul ChehabWe present here different situations in which the filtering of high or low modes is used either for stabilizing semiimplicit numerical schemes when solving nonlinear parabolic equations, or for building adapted damping operators in the case of dispersive equation. We consider numerical filtering provided by mutigridlike techniques as well as the filtering resulting from operator with monotone symbols

Numerical solutions for a Timoshenkotype system with thermoelasticity with second sound Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210114
Makram Hamouda, Ahmed Bchatnia, Mohamed Ali AyadiWe consider in this article a nonlinear vibrating Timoshenko system with thermoelasticity with second sound. We first recall the results obtained in [2] concerning the wellposedness, the regularity of the solutions and the asymptotic behavior of the associated energy. Then, we use a fourthorder finite difference scheme to compute the numerical solutions and we prove its convergence. The energy decay

Nontrivial solutions for the fractional Laplacian problems without asymptotic limits near both infinity and zero Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210114
Yutong Chen, Jiabao SuIn this paper we obtain the existence of nontrivial solutions for the fractional Laplacian equations with the nonlinearity may fail to have asymptotic limits at zero and at infinity. We make use of a combination of homotopy invariance of critical groups and the topological version of linking methods.

Solutions to ChernSimonsSchrödinger systems with external potential Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20210114
Lingyu Li, Jianfu Yang, Jinge YangIn this paper, we consider the existence of static solutions to the nonlinear ChernSimonsSchrödinger system $ \begin{equation} \left\{\begin{array}{ll} iD_0\Psi(D_1D_1+D_2D_2)\Psi+V\Psi = \Psi^{p2}\Psi,\\ \partial_0A_1\partial_1A_0 = \frac 12i\lambda[\overline{\Psi}D_2\Psi\Psi\overline{D_2\Psi}],\\ \partial_0A_2\partial_2A_0 = \frac 12i\lambda[\overline{\Psi}D_1\Psi\Psi\overline{D_1\Psi}]

A generalization of a criterion for the existence of solutions to semilinear elliptic equations Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20201028
Pierre BarasWe prove an abstract result of existence of "good" generalized subsolutions for convex operators. Its application to semilinear elliptic equations leads to an extension of results by P.BM.Pierre concerning a criterion for the existence of solutions to a semilinear elliptic or parabolic equation with a convex nonlinearity. We apply this result to the model problem $ \Delta u = a \nabla u^p+ bu^q+f

On a linearized MullinsSekerka/Stokes system for twophase flows Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20201125
Helmut Abels, Andreas MarquardtWe study a linearized MullinsSekerka/Stokes system in a bounded domain with various boundary conditions. This system plays an important role to prove the convergence of a Stokes/CahnHilliard system to its sharp interface limit, which is a Stokes/MullinsSekerka system, and to prove solvability of the latter system locally in time. We prove solvability of the linearized system in suitable $ L^2 $Sobolev

Numerical simulation of the nonlinear fractional regularized longwave model arising in ion acoustic plasma waves Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20201125
Omid Nikan, Seyedeh Mahboubeh MolaviArabshai, Hossein JafariThis paper aimed at obtaining the travelingwave solution of the nonlinear time fractional regularized longwave equation. In this approach, firstly, the time fractional derivative is accomplished using a finite difference with convergence order $ \mathcal{O}(\delta t^{2\alpha}) $ for $ 0 < \alpha< 1 $ and the nonlinear term is linearized by a linearization technique. Then, the spatial terms are approximated

An age group model for the study of a population of trees Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20201125
Laurent Di Menza, Virginie JoanneFabreIn this paper, we derive a simple model for the description of an ecological system including several subgroups with distinct ages, in order to analyze the influence of various phenomena on temporal evolution of the considered species. Our aim is to address the question of resilience of the global system, defined as its ability to stabilize itself to equilibrium, when being perturbed by exterior fluctuations

On the convergence to equilibria of a sequence defined by an implicit scheme Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20201125
Thierry Horsin, Mohamed Ali JendoubiWe present numerical implicit schemes based on a geometric approach of the study of the convergence of solutions of gradientlike systems given in [3]. Depending on the globality of the induced metric, we can prove the convergence of these algorithms.

Representation and approximation of the polar factor of an operator on a Hilbert space Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20201125
Mostafa MbekhtaLet $ H $ be a complex Hilbert space and let $ \mathcal{B}(H) $ be the algebra of all bounded linear operators on $ H $. The polar decomposition theorem asserts that every operator $ T \in \mathcal{B}(H) $ can be written as the product $ T = V P $ of a partial isometry $ V\in \mathcal{B}(H) $ and a positive operator $ P \in \mathcal{B}(H) $ such that the kernels of $ V $ and $ P $ coincide. Then this

Improved Sobolev inequalities involving weighted Morrey norms and the existence of nontrivial solutions to doubly critical elliptic systems involving fractional Laplacian and Hardy terms Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20201125
Gongbao Li, Tao YangIn this paper, we prove two new improved Sobolev inequalities involving weighted Morrey norms in $ {\dot{H}}^s( \mathbb{R}^{n})\times {\dot{H}}^s( \mathbb{R}^{n}) $

Oscillation criteria for kernel function dependent fractional dynamic equations Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20201123
Bahaaeldin Abdalla, Thabet AbdeljawadIn this work, we examine the oscillation of a class fractional differential equations in the frame of generalized nonlocal fractional derivatives with function dependent kernel type. We present sufficient conditions to prove the oscillation criteria in both of the RiemannLiouville (RL) and Caputo types. Taking particular cases of the nondecreasing function appearing in the kernel of the treated fractional

Applying quantum calculus for the existence of solution of \begin{document}$ q $\end{document}integrodifferential equations with three criteria Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20201123
Thabet Abdeljawad, Mohammad Esmael SameiCrisis intervention in natural disasters is significant to look at from many different slants. In the current study, we investigate the existence of solutions for $ q $

Nonlinear singular \begin{document}$ p $\end{document} Laplacian boundary value problems in the frame of conformable derivative Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20201123
Mokhtar Bouloudene, Manar A. Alqudah, Fahd Jarad, Yassine Adjabi, Thabet AbdeljawadThis paper studies a class of fourth point singular boundary value problem of $ p $Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the

Stability analysis of a general HIV dynamics model with multistages of infected cells and two routes of infection Discrete Contin. Dyn. Syst. S (IF 2.425) Pub Date : 20201123
A. M. Elaiw, N. H. AlShamrani, A. AbdelAty, H. DuttaThis paper studies an $ (n+2) $dimensional nonlinear HIV dynamics model that characterizes the interactions of HIV particles, susceptible CD4$ ^{+} $ T cells and $ n $stages of infected CD4$ ^{+} $ T cells. Both virustocell and celltocell infection modes have been incorporated into the model. The incidence rates of viral and cellular infection as well as the production and death rates of all