Existence and concentration of positive solutions for non-autonomous Schrödinger-Poisson systems

In this paper, we deal with a class of non-autonomous Schrödinger-Poisson systems involving concave-convex nonlinearities and weight functions. We obtain the existence and multiplicity of positive solutions by a global compactness lemma of Schrödinger-Poisson type and Ljusternik-Schnirelmann theory. Moreover, we also conclude that the global maximum point of the solution concentrates on a local minimum point of the weight function.     

Positive solutions for a system of generalized Lidstone problems

In this paper, we study the existence and multiplicity of positive solutions for the system of the generalized Lidstone problems We use fixed point index theory to establish our main results based on a priori estimates achieved by utilizing some properties of concave functions, so that the nonlinearities f and g are allowed to grow in distinct manners, with one of them growing superlinearly and the other growing sublinearly.     

Multiple positive solutions of singularly perturbed differential systems with different orders

In this paper, we consider the multiplicity of positive solutions for a class of singular higher-order perturbed differential systems with different orders. By employing a well-known fixed point theorem, some new existence results are given under the case where nonlinearity can be sign changing.     

椭圆边值系统的正径向解的存在性与多解性

通过利用锥拉伸及锥压缩型的Krasnosel‘skii不动点定理，我们研究了一类椭圆边值系统的正径向解的存在性，非存在性与多解性。     

Two periodic solutions of neutral difference systems depending on two parameters

In this paper, we establish existence, multiplicity and nonexistence of periodic solutions for a class of first-order neutral difference systems. Our approach is based on a fixed point theorem in cones as well as some analysis techniques.     

环域上一类二阶非线性椭圆系统的正对径解

研究环域上一类非线性二阶椭圆系统的正对径解的存在性和多解性，章的主要思想是锥拉伸与锥压缩型的Krasnosel’skii不动点定理的局部应用。     

Two periodic solutions of n-dimensional neutral functional difference systems

In this paper, we establish existence, multiplicity and nonexistence of periodic solutions for a class of first-order n-dimensional neutral functional difference systems. Our approach requires the Krasnoselskii fixed point theorem in cones.     

Doubly periodic solutions to a coupled telegraph system

While the nonlinearities are bounded below, we establish the existence and multiplicity results of doubly periodic solutions for a coupled nonlinear telegraph system with a parameter. The proof is based on a well known fixed theorem in a cone.     

Local superlinearity for elliptic systems involving parameters

We study the existence, non-existence, and multiplicity of positive solutions for a class of systems of second-order ordinary differential equations using the fixed-point theorem of cone expansion/compression type, the upper-lower solutions method, and degree arguments. We apply our abstract results to study semilinear elliptic systems in bounded annular domains with non-homogeneous boundary conditions. Here the nonlinearities satisfy local superlinear assumptions.     

一类微分方程组的非齐次Sturm-Liouville边值问题解的存在性

在允许非线性项变号的情况下,利用锥上不动点定理,讨论了一类二阶非线性微分方程组的非齐次Sturm-Liouville边值问题解的存在性,得到了至少一个解及正解存在的多个存在性定理．     

On a class of semipositone discrete boundary value problems

In this paper, we deal with a class of semipositone discrete boundary value problems via critical point theory developed by Chang, and obtain nonexistence and multiplicity results on sublinear nonlinearities and an existence result on superlinear nonlinearities, respectively.     

On elliptic systems with discontinuous nonlinearities

In this paper we deal with elliptic systems with discontinuous nonlinearities. The discontinuous nonlinearities are assumed to satisfy quasimonotone conditions. We shall use the method of upper and lower solutions with fixed point theorems on increasing operators in ordered Banach spaces to show some existence theorems.     

三阶p-Laplacian非齐次边值问题多重正解的存在性

本文应用凸锥上的一个不动点定理,讨论了一类含p-Laplacian算子的三阶非齐次边值问题多重正解的存在性,得到了这类边值问题至少存在三个正解的充分条件,并给出了一个实例.     

具有变号非线性项的二阶三点边值问题的两个正解

本文首先证明双锥上的一个不动点定理，并通过该定理研究一类具有变号非线性项的二阶三点边值问题两个正解的存在性．同时，该三点边值问题相关的Green函数也被给出．     

POSITIVE PERIODIC SOLUTIONS OF THE FIRST- ORDER SINGULAR DISCRETE SYSTEMS

In this paper, we study two kinds of first-order singular discrete systems. By the fixed point index theory, we investigate the existence and multiplicity of positive periodic solutions of the systems.     

Existence, localization and multiplicity results for positive radial solutions of semilinear elliptic systems

Existence, localization and multiplicity results of positive solutions to a system of singular second-order differential equations are established by means of the vector version of Krasnoselskii's cone fixed point theorem. The results are then applied for positive radial solutions to semilinear elliptic systems.     

拓扑定理及其在超线性脉冲方程中的应用

本文研究一类含脉冲的非保守超线性方程的周期振动问题.通过详细刻画跳跃映射的角度函数,并应用相平面分析方法,本文证明方程的Poincaré映射有无穷多个不动点,而这些不动点对应了方程的无穷多个2π周期解.由于本文考虑的Poincaré映射不是同胚,所以,本文重新构造并证明了一个拓扑定理用于替代经典的Poincaré-Birkhoff扭转不动点定理.     

非线性二阶常微分方程的正周期解

讨论一类非线性二阶常微分方程的周期解问题 ,利用Banach空间锥上的不动点定理得到了正周期解的存在性和多重性结果 ,大大改进了文献 [1 ]的结果     

Exact multiplicity results for variational inequalities involving pointwise constraints on the derivatives

This paper concerns a class of nonlinear variational problems involving pointwise constraints on the second derivatives. Our aim is to describe the set of data for which these problems have solutions and to analyse the structure of the set of solutions under suitable assumptions on the asymptotic behaviour of the nonlinear term. In particular, if this term is assumed to be convex, then we can specify the number of solutions and obtain exact multiplicity results.The existence, nonexistence and multiplicity results we obtain show that the presence of constraints of this kind produces some phenomena which are typical of nonlinear elliptic equations with “jumping” nonlinearities.     

A six-point nonlocal integral boundary value problem for fractional differential equations

In this paper, we consider the existence and multiplicity of positive solutions to some class of boundary value problem for fractional differential equation of high order. Our analysis relies on the Krasnoselskii??s fixed point theorem in a cone.