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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...
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...
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 ...
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...
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...
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...
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...
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...
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...
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 ...
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 ...
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...
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...
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...
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 ...
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...
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 ...
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...
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...
The original article was published in Boundary Value Problems 2017 2017:165
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...
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....
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...
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...
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...
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...
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.
In this paper, we study the existence of multiple positive solutions to the following Kirchhoff equation with competing potential 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...
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...
We prove the existence of multiple positive solutions for a fractional Laplace problem with critical growth and sign-changing weight in non-contractible domains.
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...
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...
In this paper, we study the existence of ground state solutions to the following fractional Schrödinger system with linear and nonlinear couplings:
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...
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...
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...
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...
In this paper, the authors investigate the existence and multiplicity of solutions for the following fractional Hamiltonian system:
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...
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