Articles

Ground state solutions of Nehari–Pohožaev type for a kind of nonlinear problem with general nonlinearity and nonlocal convolution term

Authors: Shuai Yuan and Fangfang Liao

On classical solutions of Rayleigh–Taylor instability in inhomogeneous viscoelastic fluids

We study the nonlinear Rayleigh–Taylor (RT) instability of an inhomogeneous incompressible viscoelastic fluid in a bounded domain. It is well known that there exist strong solutions of RT instability in

Authors: Zhidan Tan and Weiwei Wang

Ground state solutions for fractional Schrödinger equation with variable potential and Berestycki–Lions type nonlinearity

Authors: Jing Chen and Zu Gao

A modified Schrödinger-type identity: uniqueness of solutions for singular boundary value problem for the Schrödinger equation

This paper is devoted to modifying the Schrödinger-type identity related to singular boundary value problem in (Zhang et al. in Bound. Value Probl. 2018:135, 2018). We also present some mathematical consequences ...

Authors: Hongjun He and Zhifeng Pang

Solvability for a class of integral inequalities with maxima on the theory of time scales and their applications

This paper is committed to introducing some Bihari type inequalities for scalar functions of one independent variable under an initial condition associated with an arbitrary time scale ...

Authors: Zareen A. Khan

Monotone iterative method for a p-Laplacian boundary value problem with fractional conformable derivatives

By using monotone iterative method, the extremal solutions and the unique solution are obtained for a nonlinear fractional p-Laplacian boundary value problem involving fractional conformable derivatives and nonlo...

Authors: Jianfang Qin, Guotao Wang, Lihong Zhang and Bashir Ahmad

Multiple positive solutions for mixed fractional differential system with p-Laplacian operators

This paper is focused on researching a class of mixed fractional differential system with p-Laplacian operators. Based on the properties of the corresponding Green’s function, different combinations of superlinea...

Authors: Ying Wang

Convergence rates in homogenization of p-Laplace equations

This paper is concerned with homogenization of p-Laplace equations with rapidly oscillating periodic coefficients. The main difficulty of this work is due to the nonlinear structure in this field concerning p-Lap...

Authors: Jie Zhao and Juan Wang

Multiple solutions for quasilinear elliptic problems with concave-convex nonlinearities in Orlicz–Sobolev spaces

Using variational arguments, we establish the existence of two nontrivial solutions for quasilinear elliptic problems in Orlicz–Sobolev spaces, where the nonlinear terms exhibit the combined effects of concave...

Authors: Shujun Wu

Positive solutions of fractional differential equation with two pieces in chain interval and simultaneous Dirichlet boundary conditions

In the current study, by using some fixed point technique such as Banach contraction principle and fixed point theorem of Krasnoselskii, we look into the positive solutions for fractional differential equation

Authors: Vahid Hedayati and Mohammad Esmael Samei

New general decay results in an infinite memory viscoelastic problem with nonlinear damping

Authors: Adel M. Al-Mahdi and Mohammad M. Al-Gharabli

Positive solutions for a class of nonhomogeneous Kirchhoff–Schrödinger–Poisson systems

Authors: Hongxia Shi

Boundedness in a quasilinear chemotaxis–haptotaxis model of parabolic–parabolic–ODE type

This paper deals with the boundedness of solutions to the following quasilinear chemotaxis–haptotaxis model of parabolic–parabolic–ODE type:

Authors: Long Lei and Zhongping Li

A study on the thermoelasticity of three-phase-lag dipolar materials with voids

With a wide applicability in solid state mechanics, the theory of continuous dipolar materials with voids is a distinctive part of microstructure theory, a theory that emerged with the necessity of eliminating...

Authors: Lavinia Codarcea-Munteanu and Marin Marin

Multiple positive solutions for quasilinear elliptic problems with combined critical Sobolev–Hardy terms

In this paper, we investigate the quasilinear elliptic equations involving multiple critical Sobolev–Hardy terms with Dirichlet boundary conditions on bounded smooth domains  ...

Authors: Yuanyuan Li

Existence of nonconstant periodic solutions for \(p(t)\)-Laplacian Hamiltonian system

Authors: Yuanfang Ru and Fanglei Wang

Qualitative properties for a pseudo-parabolic equation with nonlocal reaction term

This paper deals with the qualitative properties of solutions for null Neumann initial boundary value problem to a nonlocal pseudo-parabolic equation in the sense of ...

Authors: Yadong Zheng and Zhong Bo Fang

Local pseudo almost automorphic functions with applications to semilinear dynamic equations on changing-periodic time scales

In this paper, based on the concepts of changing-periodic time scales, we introduce a notion of local pseudo almost automorphic functions on an arbitrary time scale with a bounded graininess function μ. Then, som...

Authors: Chao Wang, Ravi P. Agarwal, Donal O’Regan and Rathinasamy Sakthivel

Direct and inverse problem for geometric perturbation of the Laplace operator in a strip

This paper is concerned with the inverse problem of determining geometric shape of a part γ of the boundary of a perturbed strip Ω from a pair of Cauchy data of a harmonic function u in Ω. This leads to the study...

Authors: I. Khélifa and L. Chorfi

Construction of singular limits for a strongly perturbed four-dimensional Navier problem with exponentially dominated nonlinearity and nonlinear terms

Authors: Sami Baraket, Souhail Chebbi and Nejmeddine Chorfi

A reduced fourth-order compact difference scheme based on a proper orthogonal decomposition technique for parabolic equations

In this paper, we present a reduced high-order compact finite difference scheme for numerical solution of the parabolic equations. CFDS4 is applied to attain high accuracy for numerical solution of parabolic e...

Authors: Baozou Xu and Xiaohua Zhang

Stability and Hopf bifurcation of a predator-prey model

In this paper, we study a class of predator-prey model with Holling-II functional response. Firstly, by using linearization method, we prove the stability of nonnegative equilibrium points. Secondly, we obtain...

Authors: Fan Wu and Yujuan Jiao

On an electrorheological fluid equation with orientated convection term

Authors: Huashui Zhan

Existence and uniqueness for some equation of a mixed elliptic-hyperbolic type

In the paper, we prove results on existence and uniqueness of weak solutions for closed Dirichlet problem for a transonic flow model, and interior regularity results are also given in the important special cas...

Authors: Zhang Haixia and Xiao Wei

Bound and ground states for a class of Schrödinger–Poisson systems

Authors: Fubao Zhang and Li Cai

Existence of nontrivial weak solutions for p-biharmonic Kirchhoff-type equations

Authors: Jung-Hyun Bae, Jae-Myoung Kim, Jongrak Lee and Kisoeb Park

Multiple solutions to the Kirchhoff fractional equation involving Hardy–Littlewood–Sobolev critical exponent

In this paper, we study a fractional Kirchhoff type equation with Hardy–Littlewood–Sobolev critical exponent. By using variational methods, we obtain the existence of mountain-pass type solution and negative e...

Authors: Jichao Wang, Jian Zhang and Yujun Cui

Nonlinear boundary value problems of a class of elliptic equations involving critical variable exponents

In this paper, we first obtain the existence of solutions for a class of elliptic equations involving critical variable exponents and nonlinear boundary values by the mountain pass theorem and concentration co...

Authors: Yingying Shan and Yongqiang Fu

New proof on exponential convergence for cellular neural networks with time-varying delays

In this paper, we deal with a class of cellular neural networks with time-varying delays. Applying differential inequality strategies without assuming the boundedness conditions on the activation functions, we...

Authors: Changjin Xu and Peiluan Li

The finite speed of propagation for solutions to stochastic viscoelastic wave equation

Authors: Fei Liang and Zhe Hu

Boundedness in a quasilinear attraction–repulsion chemotaxis system with nonlinear sensitivity and logistic source

Authors: Lijun Yan and Zuodong Yang

Periodic solutions for nonlocal \(p(t)\)-Laplacian systems

Authors: Shengui Zhang

Existence and multiplicity of solutions for second-order Hamiltonian systems satisfying generalized periodic boundary value conditions at resonance

We investigate the existence and multiplicity of solutions for second-order Hamiltonian systems satisfying generalized periodic boundary value conditions at resonance by means of the index theory, the critical...

Authors: Mingliang Song

A coupled system of fractional differential equations on the half-line

Authors: Chengbo Zhai and Jing Ren

Invariant tori for a nonlinearly modified Kawahara equation with periodic boundary conditions

Authors: Li Yin, Lufang Mi, Wenyan Cui and Xiuli Lin

A linear, stabilized, non-spatial iterative, partitioned time stepping method for the nonlinear Navier–Stokes/Navier–Stokes interaction model

In this paper, a linear, stabilized, non-spatial iterative, partitioned time stepping method is developed and studied for the nonlinear Navier–Stokes/Navier–Stokes interaction. A backward Euler scheme is utili...

Authors: Jian Li, Pengzhan Huang, Jian Su and Zhangxin Chen

The numerical solution of forward and inverse Robin problems for Laplace’s equation

The Robin boundary value problem for Laplace’s equation in the elliptic region (which is a forward problem) and its related inverse problem can be used to reconstruct Robin coefficients from measurements on a ...

Authors: Dan Qu and Yan-Bo Ma

Unique iterative positive solutions for a singular p-Laplacian fractional differential equation system with infinite-point boundary conditions

By using the method of mixed monotone operator, a unique positive solution is obtained for a singular p-Laplacian boundary value system with infinite-point boundary conditions in this paper. Green’s function is d...

Authors: Limin Guo and Lishan Liu

A singular fractional Kelvin–Voigt model involving a nonlinear operator and their convergence properties

In this paper, we focus on a generalized singular fractional order Kelvin–Voigt model with a nonlinear operator. By using analytic techniques, the uniqueness of solution and an iterative scheme converging to t...

Authors: Jianxin He, Xinguang Zhang, Lishan Liu, Yonghong Wu and Yujun Cui

Philos-type oscillation criteria for second-order linear impulsive differential equation with damping

In this paper, the problem of oscillation for a second-order linear impulsive differential equation with damping is investigated. This equation can be more accurately used to model the states of many evolution...

Authors: Kunwen Wen, Yuping Zeng, Huaqin Peng and Lifang Huang

A global compactness result for a critical nonlinear Choquard equation in \(\mathbb{R} ^{N}\)

Authors: Wangcheng Huang, Wei Long, Aliang Xia and Xiongjun Zheng

Fractional order differential systems involving right Caputo and left Riemann–Liouville fractional derivatives with nonlocal coupled conditions

In this paper, we introduce and study a new kind of coupled fractional differential system involving right Caputo and left Riemann–Liouville fractional derivatives, supplemented with nonlocal three-point coupl...

Authors: Bashir Ahmad, Sotiris K. Ntouyas and Ahmed Alsaedi

Quasi-periodic solutions for nonlinear wave equation with singular Legendre potential

Authors: Guanghua Shi and Dongfeng Yan

Parametric investigation of the Nernst–Planck model and Maxwell’s equations for a viscous fluid between squeezing plates

The Poisson–Boltzmann equation is derived from the assumption of thermodynamic equilibrium where the ionic distribution is not affected by fluid flow. Although this is a reasonable assumption for steady electr...

Authors: Muhammad Sohail Khan, Rehan Ali Shah, Amjad Ali and Aamir Khan

\((\omega ,c)\)-Pseudo periodic functions, first order Cauchy problem and Lasota–Wazewska model with ergodic and unbounded oscillating production of red cells

Authors: Edgardo Alvarez, Samuel Castillo and Manuel Pinto

Boundary value problem for a class of fractional integro-differential coupled systems with Hadamard fractional calculus and impulses

This paper considers the boundary value problem for a class of fractional integro-differential coupled systems with Hadamard fractional calculus and impulses. Some sufficient conditions of the existence and un...

Authors: Kaihong Zhao, Leping Suo and Yongzhi Liao

The Keller–Osserman-type conditions for the study of a semilinear elliptic system

Authors: Dragos-Patru Covei

Multiplicity results for biharmonic equations involving multiple Rellich-type potentials and critical exponents

In this paper, a biharmonic equation is investigated, which involves multiple Rellich-type potentials and a critical Sobolev exponent. By using variational methods and analytical techniques, the existence and ...

Authors: Jinguo Zhang and Tsing-San Hsu

Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey model

In this paper, Turing patterns and steady state bifurcation of a diffusive Beddington–DeAngelis-type predator–prey model with density-dependent death rate for the predator are considered. We first investigate ...

Authors: Hongwu Xu and Shengmao Fu

Existence and uniqueness of solutions for mixed fractional q-difference boundary value problems

In this paper, we investigate the existence and uniqueness of solutions for mixed fractional q-difference boundary value problems involving the Riemann–Liouville and the Caputo fractional derivative. By using the...

Authors: Lulu Zhang and Shurong Sun