POSITIVE SOLUTIONS OF m-POINT BOUNDARY-VALUE PROBLEMS

The paper is concerned with the existence and multiplicity of positive solutions for a nonlinear m-point boundary value problem. The proofs are based on a fixed-point theorem and a fixed-point index theorem in cones.     

The existence of countably many positive solutions for singular multipoint boundary value problems

In this paper, we study the existence of countably many positive solutions for a singular multipoint boundary value problem. By using fixed-point index theory and the Leggett-Williams’ fixed-point theorem, sufficient conditions for the existence of countably many positive solutions are established.     

Fractional Differential Equations with Anti-Periodic Boundary Conditions

We are concerned with the existence of solutions of a class of fractional differential equations with anti-periodic boundary conditions involving the Caputo fractional derivative. We give two results: the first is based on Banach's fixed-point theorem, and the second is based on Schauder's fixed-point theorem.     

Existence of Positive Solutions for Second-Order Impulsive Boundary Value Problems on Time Scales

In this paper, by using Leray–Schauder fixed-point theorem, Avery–Henderson fixed-point theorem and Leggett–Williams fixed-point theorem, respectively, we investigate the conditions for the existence of at least one, two and three positive solutions to nonlinear second-order impulsive boundary value problems on time scales.     

POSITIVE SOLUTIONS FOR p-LAPLACIAN DYNAMIC EQUATIONS ON TIME SCALES

The three-point boundary value problems of p-Laplacian dynamic equations on time scales are investigated. By using Krasnosel＇skii＇s fixed-point theorem and fixed-point index theorem, criteria are achieved for the existence of at least one, two or 2n positive solutions. Furthermore, some examples are included to illustrate the main theorems.     

MULTIPLE POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF DELAY DIFFERENTIAL EQUATIONS WITH DENUMBERABLE SINGULARITIES ON INFINITE INTERVAL

This paper deals with the existence of denumberable positive solutions to boundary value problems of delay differential equations with denumberable singularities on infinite intervals. By the fixed-point index theory and a new fixed-point theorem in cones, the existence of denumberable positive solutions is obtained under some suitable growth conditions imposed on the nonlinear term.     

二阶Hopfield神经网络周期解的存在性

本文讨论了一类带有时滞的二阶Hopfield神经网络周期解的存在性问题。首先利用Brouwer不动点定理证明了平衡点的存在性,通过平衡点和拉格朗日中值定理,将高阶神经网络模型转换为一阶模型,然后利用重合度理论给出了周期解存在的充分条件。     

MULTIPLE PERIODIC SOLUTIONS TO SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATION WITH INFINITE DELAY

This paper is concerned with the existence of positive periodic solutions to a second order functional differential equation with infinite delay.Under the appropriate conditions,some existence and multiplicity of positive periodic solutions are derived by an abstract fixed-point theorem.     

带有外部输入项的时间周期SIR传染病模型的周期行波解北大核心CSCD

研究了一类带有外部输入项的时间周期SIR传染病模型周期行波解的存在性和不存在性.首先,通过构造辅助系统适当的上下解并定义闭凸锥,将周期行波解的存在性转化为定义在这个闭凸锥上的非单调算子的不动点问题,利用Schauder不动点定理建立辅助系统周期解的存在性,并利用Arzela-Ascoli定理证明了原模型周期行波解的存在性.其次,借助分析技术得到了周期行波解的不存在性.     

A computer-assisted proof of the existence of traveling wave solutions to the scalar Euler equations with artificial viscosity

We establish the existence and local uniqueness of traveling wave solutions to the one-dimensional Euler equations with artificial viscosity. The equations are expressed as a fixed-point problem, which is solved by a computer-assisted method based on Yamamoto’s application of the Banach fixed-point theorem.     

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS TO A SECOND-ORDER DIFFERENTIAL INCLUSION

In this paper,the existence of positive periodic solutions to a second-order differential inclusion is considered.Some existence results are established by the fixed-point theorem for multivalued operators and Sobolev constant.     

Existence of positive periodic solutions of impulsive functional differential equations with two parameters

In this paper, we employ a well-known fixed-point index theorem to study the existence and non-existence of positive periodic solutions for the periodic impulsive functional differential equations with two parameters. Several existence and non-existence results are established.     

一类p-Laplacian方程四点边值问题正解的存在性

利用范数形式的锥拉伸与压缩不动点定理,讨论了一类p-Laplacian方程四点边值问题,获得了正解的存在性定理.     

一类时滞积分方程概周期解的存在性

本文讨论一类具广泛应用背景的概周期时滞积分方程,利用极限方程理论和不动点定理等方法,给出了关于概周期解的几个存在性定理.     

一类具P-Laplacian算子四阶两点边值问题正解的存在性

利用Leggett-Williams不动点定理研究了一类具有P-Laplacian算子的边值问题,得到了三个正解存在性的一组充分条件.     

一类具p-Laplacian算子边值问题的三个正解的存在性

利用Leggett-Williams不动点定理研究了一类具p-Laplacian算子的边值问题,得到了三个正解存在的一组充分条件.     

Periodic positive solutions for adelay nonlinear differential equation with piecewise constant arguments

Using a fixed-point theorem in cone, existence criteria are proved for the periodic positive solutions of a delay differential equation with piecewise constant arguments. Several examples concerning biological models for the survival of red blood cells are given.     

四阶边值问题正解的存在性与多解性

本文讨论了非线性四阶边值问题u^(4)(t)=φ（t）f(u(t),u“(t),t∈(0,1),u(0)=u(1)=u“(0) =u“(1)=0正确的存在性，其中φ（t)∈C([0,1],[0,∞)),f(u,v)∈C（[0,∞],[0,∞))。利用锥压缩与锥拉伸不动点定理，给出了该问题正解存在与多个正解存在的充分条件。     

四阶微分方程三点边值问题三个正解的存在性

在四阶微分方程非线性项f中含有未知函数“的二阶导数u”的情况下,运用Avery-Peterson不动点定理,研究了一类四阶微分方程三点边值问题三个正解的存在性,得到了该类边值问题存在三个正解的充分条件．     

Existence of solutions of neutral functional integrodifferential equation in Banach spaces

In this paper we prove the existence of mild solutions for neutral functional integrodifferential equation in a Banach space. The results are obtained by using the Schaefer fixed-point theorem.