Existence and multiplicity of solutions to a singular elliptic system with critical Sobolev–Hardy exponents and concave–convex nonlinearities

This paper is concerned with a singular elliptic system, which involves the Caffarelli–Kohn–Nirenberg inequality and critical Sobolev–Hardy exponents. The existence and multiplicity results of positive solutions are obtained by variational methods.     

Positive steady state solutions of a Leslie–Gower predator–prey model with Holling type II functional response and density-dependent diffusion

In this paper, we consider a Leslie–Gower predator–prey model with Holling type II functional response and density-dependent diffusion under zero Dirichlet boundary condition. Using degree theory, bifurcation theory, energy estimates and asymptotical behavior analysis, the existence and multiplicity of positive steady state solutions were shown under certain conditions on the parameters.     

非线性参数椭圆系统正解的存在性与多解性

本文讨论了一类非线性含参数椭圆系统正解的存在性与多解性,通过线性算子的谱半径,给出其正径向解存在与多解的条件,本质上改进和推广了文[1－3]的结果．     

时间标度上的动态方程周期边值问题的正解

讨论了时间标度上一类二阶非线性动态方程的周期边值问题正解以及多解的存在性,利用锥上的不动点理论给出了简捷的判别方法并举例。     

On a Schrödinger–Kirchhoff-type equation involving the p(x)-Laplacian

In this paper we deal with a Schrödinger-type equation involving a nonlocal Kirchhoff-type coefficient and depending on two real parameters. Working within the framework of variable exponent spaces and using the variational approach, we obtain several results of existence and multiplicity of solutions, depending on the range of the parameters.     

Multiple solutions for a class of biharmonic elliptic systems with Sobolev critical exponent

In this paper, we study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic systems with Sobolev critical exponent in a bounded domain. By using the variational method and the Nehari manifold, we obtain the existence and multiplicity results of nontrivial solutions for the systems.     

MULTIPLE SYMMETRIC RESULTS FOR A CLASS OF BIHARMONIC ELLIPTIC SYSTEMS WITH CRITICAL HOMOGENEOUS NONLINEARITY IN R~N

This paper is dedicated to studying the existence and multiplicity of symmetric solutions for a class of biharmonic elliptic systems with critical homogeneous nonlinearity in RN. By virtue of variational methods and the symmetric criticality principle of Palais,we establish several existence and multiplicity results of G-symmetric solutions under certain appropriate hypotheses on the parameters and the weighted functions.     

一类奇异四阶方程组边值问题的多重正解

该文应用不动点指数理论,研究了一类奇异非线性四阶微分方程组的两点边值问题,通过相应线性问题的第一特征值建立了其正解的存在性与多解性定 理,在本质上改进和推广了［1］的结论.     

Multiplicity of solutions for a class of Schrödinger–Maxwell systems

In this paper, we study existence and multiplicity of nontrivial solutions for a class of Schrödinger–Maxwell systems via variational methods. Some new existence results of nontrivial solutions are obtained.     

二阶非线性常微分方程的正周期解

本文应用Ｋｒａｓｎｏｓｅｌｓｋｉｉ锥映射不动点定理，研究了二阶非线性常微分方程的ω-周期解的存在性，获得了若干正ω-周期解的存在性与多重性结果．