Articles

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

Existence of multiple positive solutions for fractional Laplace problems with critical growth and sign-changing weight in non-contractible domains

We prove the existence of multiple positive solutions for a fractional Laplace problem with critical growth and sign-changing weight in non-contractible domains.

Authors: Lu Pang, Xueqin Li and Yajing Zhang

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

Existence of ground state solutions to a class of fractional Schrödinger system with linear and nonlinear couplings

In this paper, we study the existence of ground state solutions to the following fractional Schrödinger system with linear and nonlinear couplings:

Authors: Xinsheng Du and Anmin Mao

Existence theory to a class of boundary value problems of hybrid fractional sequential integro-differential equations

In this article, we study the existence result for a boundary value problem (BVP) of hybrid fractional sequential integro-differential equations. A fixed point theorem provided by Dhage in (Nonlinear Anal. 4:4...

Authors: M. Jamil, R. A. Khan and K. Shah

Properties of Green’s function and the existence of different types of solutions for nonlinear fractional BVP with a parameter in integral boundary conditions

This paper is concerned with the impact of the parameter on the existence of different types of solutions for a class of nonlinear fractional integral boundary value problems with a parameter that causes the s...

Authors: Wenxia Wang

Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in \(\mathbb{R}^{3}\)

Authors: Da-Bin Wang, Tian-Jun Li and Xinan Hao

Synchronization results for a class of fractional-order spatiotemporal partial differential systems based on fractional Lyapunov approach

In this paper, the problem of synchronization of a class of spatiotemporal fractional-order partial differential systems is studied. Subject to homogeneous Neumann boundary conditions and using fractional Lyap...

Authors: Adel Ouannas, Xiong Wang, Viet-Thanh Pham, Giuseppe Grassi and Van Van Huynh

On the connection problem for nonlinear differential equation

Authors: Zhao-Yun Zeng and Lin Hu

The wave equation with locally distributed control in non-cylindrical domain

This paper is concerned with exact internal controllability for a one-dimensional wave equation in a non-cylindrical domain. This equation characterizes the motion of a string with a fixed endpoint and the oth...

Authors: Lizhi Cui

Existence and multiplicity of solutions for fractional Hamiltonian systems

In this paper, the authors investigate the existence and multiplicity of solutions for the following fractional Hamiltonian system:

Authors: Guoqing Chai and Weiming Liu

Comparison of two projection methods for the solution of frictional contact problems

Frictional contact problems in linear elasticity are considered in this paper. The contact constraint is imposed in the weak sense using the fixed point method, which leads to a variational equation problem. F...

Authors: Shougui Zhang and Ruisheng Ran

Conjugate boundary value problems with functional boundary conditions at resonance

By constructing a suitable projection scheme and using the coincidence degree theory of Mawhin, we study the existence of solutions for conjugate boundary value problems with functional boundary conditions at ...

Authors: Weihua Jiang, Jing Qiu and Bingzhi Sun

Asymptotic behavior of solutions to a class of coupled nonlinear parabolic systems

This paper studies the Cauchy problem to a class of coupled nonlinear parabolic systems and investigates the asymptotic behavior of solutions to the problem. The blow-up theorem of Fujita type is established b...

Authors: Yan Leng, Yuanyuan Nie and Qian Zhou

Blow-up of solution for quasilinear viscoelastic wave equation with boundary nonlinear damping and source terms

In this paper, we consider the blow-up result of solution for a quasilinear viscoelastic wave equation with strong damping and boundary nonlinear damping. We prove a finite time blow-up result of solution with...

Authors: Mi Jin Lee, Jum-Ran Kang and Sun-Hye Park

Asymptotic boundary estimates for solutions to the p-Laplacian with infinite boundary values

In this paper, by using Karamata regular variation theory and the method of upper and lower solutions, we mainly study the second order expansion of solutions to the following p-Laplacian problems:

Authors: Ling Mi

Positive solutions of semilinear problems in an exterior domain of \(\mathbb{R}^{2}\)

The aim of this paper is to establish the existence and global asymptotic behavior of a positive continuous solution for the following semilinear problem:

Authors: Imed Bachar, Habib Mâagli and Said Mesloub

Infinitely many geometrically distinct solutions for periodic Schrödinger–Poisson systems

Authors: Jing Chen and Ning Zhang

A reduced-order extrapolating collocation spectral method based on POD for the 2D Sobolev equations

In this paper, we mainly use a proper orthogonal decomposition (POD) to reduce the order of the coefficient vectors of the solutions for the classical collocation spectral (CS) method of two-dimensional (2D) S...

Authors: Shiju Jin and Zhendong Luo

Infinitely many solutions for fractional Schrödinger equation with potential vanishing at infinity

Authors: Yongzhen Yun, Tianqing An, Jiabin Zuo and Dafang Zhao

Existence results for the general Schrödinger equations with a superlinear Neumann boundary value problem

The main goal of this paper is to study the general Schrödinger equations with a superlinear Neumann boundary value problem in domains with conical points on the boundary of the bases. First the formulation an...

Authors: Zhen Liu

Schrödinger-type identity to the existence and uniqueness of a solution to the stationary Schrödinger equation

In this article we study applications of the Schrödinger-type identity for obtaining transmutations via the fixed point index for nonlinear integral equations. It is possible to derive a wide range of transmut...

Authors: Delin Sun

The existence and Hyers–Ulam stability of solution for an impulsive Riemann–Liouville fractional neutral functional stochastic differential equation with infinite delay of order \(1<\beta<2\)

This paper deals with the existence of solution for an impulsive Riemann–Liouville fractional neutral functional stochastic differential equation with infinite delay of order ...

Authors: Yuchen Guo, Xiao-Bao Shu, Yongjin Li and Fei Xu

Liouville type theorem for a singular elliptic equation with finite Morse index

This paper considers the nonexistence of solutions for the following singular quasilinear elliptic problem:

Authors: Zonghu Xiu, Jing Zhao, Jianyi Chen and Hongwei Yang

Multiplicity of periodic bouncing solutions for generalized impact Hamiltonian systems

Authors: Delong Huang and Fei Guo

Multiplicity results for p-Laplacian boundary value problem with jumping nonlinearities

We investigate the multiplicity of solutions for one-dimensional p-Laplacian Dirichlet boundary value problem with jumping nonlinearities. We obtain three theorems: The first states that there exists exactly one ...

Authors: Tacksun Jung and Q-Heung Choi

Existence and asymptotic properties of positive solutions for a general quasilinear Schrödinger equation

By a change of variables with cut-off functions, we study the existence and the asymptotic behavior of positive solutions for a general quasilinear Schrödinger equation which arises from plasma physics. We ext...

Authors: Xiang Zhang and Yimin Zhang

A further study on the coupled Allen–Cahn/Cahn–Hilliard equations

In this paper, we will show that solutions of the initial boundary value problem for the coupled system of Allen–Cahn/Cahn–Hilliard equations continuously depend on parameters of the system, and under some res...

Authors: Jiaqi Yang and Changchun Liu

The obstacle problem for nonlinear noncoercive elliptic equations with \(L^{1}\)-data

Authors: Jun Zheng and Leandro S. Tavares

Retraction Note: Velocity and shear stress for an Oldroyd-B fluid within two cylinders

The Editors-in-Chief are retracting this article [1] because it overlaps with previously published articles [2,3]. None of the authors have responded to correspondence about this retraction.

Authors: Shin Min Kang, Waqas Nazeer, Muhammad Athar, Muhammad Danial Hisham and Young Chel Kwun

Laplace’s equation with concave and convex boundary nonlinearities on an exterior region

Authors: Jinxiu Mao, Zengqin Zhao and Aixia Qian

Multiplicity of solutions for a class of \((p_{1},p_{2},\ldots,p_{n})\)-Laplacian elliptic systems with a nonsmooth potential

Authors: Ziqing Yuan, Yan Wang and Sheng Liu

Nonlinear sum operator equations and applications to elastic beam equation and fractional differential equation

Authors: Yanbin Sang and Yan Ren

A new approach to convergence analysis of linearized finite element method for nonlinear hyperbolic equation

We study a new way to convergence results for a nonlinear hyperbolic equation with bilinear element. Such equation is transformed into a parabolic system by setting the original solution u as ...

Authors: Junjun Wang and Lijuan Guo

Forced oscillation of fractional differential equations via conformable derivatives with damping term

Based on the properties of nonlocal fractional calculus generated by conformable derivatives, we establish some sufficient conditions for oscillation of all solutions for fractional differential equations with...

Authors: Aphirak Aphithana, Sotiris K. Ntouyas and Jessada Tariboon