Articles

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

Solvability for a class of nonlinear Hadamard fractional differential equations with parameters

In this paper, we investigate a class of boundary value problem of nonlinear Hadamard fractional differential equations with p-Laplacian operator. By means of the properties of the Green’s functions and Guo–Krasn...

Authors: Meshari Alesemi

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

Solvability for boundary value problem of the general Schrödinger equation with general superlinear nonlinearity

This paper is mainly concerned with the boundary value problems for the general Schrödinger equation with general superlinear nonlinearity introduced in (Sun et al. in J. Inequal. Appl. 2018:100, 2018). We firstl...

Authors: Hongjun He and Zhifeng Pang

Riemann–Hilbert problems with shift on the Lyapunov curve for null-solutions of iterated Beltrami equations

In this article, we study some Riemann–Hilbert problems with shift on the Lyapunov curve for generalized polyanalytic functions, which are null-solutions of a class of iterated Beltrami equations. Firstly, we ...

Authors: Guoan Guo, Chenkai Jin, Pei Dang and Zhihua Du

Existence of solution for p-Laplacian boundary value problems with two singular and subcritical nonlinearities

We consider a boundary value problem for p-Laplacian systems with two singular and subcritical nonlinearities. We obtain one theorem which shows that there exists at least one nontrivial weak solution for these p...

Authors: Q-Heung Choi and Tacksun Jung

Convergence rates of nonlinear Stokes problems in homogenization

In this paper, we study the convergence rates of solutions in homogenization of nonlinear Stokes Dirichlet problems. The main difficulty of this work is twofold. On the one hand, the nonlinear Stokes problems ...

Authors: Juan Wang and Jie Zhao

The stability of an equation from mathematical finance without the boundary value condition

Authors: Zhan Huashui

Finite difference method for boundary value problem for nonlinear elliptic equation with nonlocal conditions

In the paper the convergence of a finite difference scheme for two-dimensional nonlinear elliptic equation in the rectangular domain with the integral boundary condition is considered. The majorant is construc...

Authors: Mifodijus Sapagovas, Olga Štikonienė, Kristina Jakubėlienė and Regimantas Čiupaila

Retraction Note: New Riesz representations of linear maps associated with certain boundary value problems and their applications

The Editors-in-Chief have retracted this article [1] because the results of the article are invalid. The article also shows significant overlap with an article by Tan et al. [2] that was simultaneously under c...

Authors: Wei Yang, Jiannan Duan, Wenmin Hu and Jing Zhang

Existence and multiplicity of positive solutions for a class of singular fractional nonlocal boundary value problems

In this article, we consider a class of singular fractional differential equations with nonlocal boundary value conditions. The existence and multiplicity of positive solutions are derived by the fixed point i...

Authors: Yongqing Wang

Minimal thinness with respect to the Schrödinger operator and its applications on singular Schrödinger-type boundary value problems

The application of the new criteria for minimally thin sets with respect to the Schrödinger operator to an approximate solution of singular Schrödinger-type boundary value problems are discussed in this study....

Authors: Bo Meng

A posteriori error estimates for fourth order hyperbolic control problems by mixed finite element methods

In this paper, we consider the a posteriori error estimates of the mixed finite element method for the optimal control problems governed by fourth order hyperbolic equations. The state is discretized by the or...

Authors: Chunjuan Hou, Zhanwei Guo and Lianhong Guo

About finite energy solutions in thermoelasticity of micropolar bodies with voids

Our study is dedicated to the problem with initial and boundary conditions in the theory of thermoelasticity for micropolar materials with pores. We obtain some results regarding the existence and uniqueness o...

Authors: Marin Marin, Adina Chirila, Andreas Öchsner and Sorin Vlase

Existence and convergence results of meromorphic solutions to the equilibrium system with angular velocity

We study the equilibrium system with angular velocity for the prey. This system is a generalization of the two-species equilibrium model with Neumann type boundary condition. Firstly, we consider the asymptoti...

Authors: Bo Meng

On the connection between two equilibrium problems for cracked bodies in the cases of thin and volume rigid inclusions

We consider equilibrium problems for an inhomogeneous two-dimensional body with a crack and a rigid inclusion. The matrix of the body is assumed to be elastic. The boundary condition on the crack curve is an i...

Authors: Nyurgun Lazarev and Galina Semenova

Multiple radial solutions for Dirichlet problem involving two mean curvature equations in Euclidean and Minkowski spaces

In this paper, we establish the existence of multiple positive radial solutions for the Dirichlet problem involving two mean curvature equations of spacelike graphs in Euclidean and Minkowski spaces.

Authors: Yaning Wang

Multiple positive solutions to Kirchhoff equations with competing potential functions in \(\mathbb{R}^{3}\)

In this paper, we study the existence of multiple positive solutions to the following Kirchhoff equation with competing potential functions:

Authors: Dongdong Sun

A generalization of the compression cone method for integral operators with changing sign kernel functions

In this paper, a new class of order cones in the space of continuous functions is introduced. The result unifies some previous work in studying the existence of solutions for differential equations using the c...

Authors: Ankai Liu and Wenying Feng

Solvability for fully cantilever beam equations with superlinear nonlinearities

Authors: Yongxiang Li and Xuechun Chen

Optimal decay result for Kirchhoff plate equations with nonlinear damping and very general type of relaxation functions

In this paper, we consider plate equations with viscoelastic damping localized on a part of the boundary and nonlinear damping in the domain. We establish general and optimal decay rate results for a wider cla...

Authors: Adel M. Al-Mahdi

The implementation of the mortar spectral element discretization of the heat equation with discontinuous diffusion coefficient

We propose to implement the mortar spectral elements discretization of the heat equation in a bounded two-dimensional domain with a piecewise continuous diffusion coefficient. The discretization on time is bas...

Authors: Mohamed Abdelwahed and Nejmeddine Chorfi

On fractional integro-differential inclusions via the extended fractional Caputo–Fabrizio derivation

We first show that four fractional integro-differential inclusions have solutions. Also, we show that dimension of the set of solutions for the second fractional integro-differential inclusion problem is infin...

Authors: Dumitru Baleanu, Shahram Rezapour and Zohreh Saberpour