带有凹凸非线性项的Klein-Gordon-Maxwell系统解的存在性和多重性

研究一类Klein-Gordon-Maxwell系统解的存在性和多重性.当非线性项是凹凸非线性项时,利用变分方法获得了系统解的存在性和多重性结果,并完善了此系统解的存在性的已有结果.     

一类泛函微分方程反周期解的存在性

研究了一类含参泛函微分方程反周期解的存在性.获得了当参数在一定范围取值时反周期解的存在性结果,得到了反周期解存在的充分条件,并通过例子表明结果的可行性.主要工具为Leray-Schauder非线性抉择.     

奇异半线性椭圆问题解的存在与不存在性(英文)

本文研究了奇异半线性椭圆问题.利用上下解方法,获得了该问题解的一个存在性和不存在性结果.     

一类时滞微分系统的周期解

研究了一类具分布时滞的一阶微分系统的周期解的存在性和全局吸引性.先通过利用重合度理论中的Mawhin延拓定理讨论了周期解的存在性,建立了一些判断准则;进而通过构造适当的Lyapunov泛函以及周期解的存在性结果研究了该类时滞微分系统的周期解的全局吸引性,获得了保证其周期解全局吸引的充分性条件.     

具有时滞的Rayleigh方程周期解的存在性与唯一性

本文研究了具有偏差变元的Rayleigh方程周期解的存在性和唯一性.利用Mawhin连续性定理,得到了该方程周期解存在性和唯一性的新结果,改进了一些已有结果.     

一类二阶差分方程边值问题解的存在性（英文）

本文研究了一个二阶差分方程边值问题解的存在性问题.利用临界点理论和变分方法,获得了几个解的存在性结果,推广了一些现有的结果.     

Banach空间二阶周期边值问题的一种拟上下解方法

利用比较结果,通过构造L-拟上下解的单调迭代过程,在L-拟上下解反序的情形下,研究了Banach空间二阶周期边值问题解的存在性,并获得该问题解的存在性与唯一性结果.     

带有非线性记忆的阻尼双曲方程组全局解的存在性与非存在性

首先研究了带有非线性记忆的双曲方程组解的局部存在性.然后,在N=1的情况下,证明了小初值解的全局存在性,并给出了当t→∞时的渐近性态.最后在N≥1且初值是正的情况下,导出了全局解的非存在性结果.     

广义Davey-Stewartson方程组的整体解及自相似解

本文研究Dalvey-Stewartson方程组的整体解与自相似解的存在性.首先,运用Ba- nach不动点定理得到一个关于解整体存在性的一般性定理,然后把一类特殊的初始值用到该存在性结果上去从而得到自相似解存在的结论.     

Banach空间二阶积分-微分方程两点边值问题的解

利用Darbo不动点定理的一般化结果以及一个脉冲积分不等式,研究Banach空间二阶混合型积分-微分方程两点边值问题解的存在性,获得了其解的两个存在性结果.并给出了一个应用例子.     

On the Existence of Solutions of Quasi-equilibrium Problems with Constraints

The quasi-equilibrium problems with constraints are formulated and some sufficient conditions on the existence of their solutions are shown. As special cases, we obtain several results on the existence of solutions of some vector quasivariational inequality and vector optimization problems. An application of the obtained results is given to show the existence of solutions of quasi-optimization problems with constraints.     

非正非线性算子方程正解的存在性及其应用

首先使用全局分歧理论得到了含参数非线性算子方程解集无界连通分支存在的结果,然后根据算子的正连通性得到了一类非正非线性算子方程正解的存在结果.使用本文的主要结果在无需假设非线性项为正的条件下可以得到某些微分边值问题正解的存在结果.     

二阶时滞微分方程边值问题的上下解方法

主要利用上下解方法和Schauder不动点定理,研究一类二阶时滞微分方程边值问题的正解存在性.为了验证结论的正确性,本文在结尾部分给出了两个例子.     

概周期解的存在性、唯一性与稳定性

本文给出了一些保证微分方程的周期解和概周期解的存在性、唯一性、稳定性与不稳定性的充分性条件及周期解的存在范围估计式.所得结果推广[1]的主要结果及[2-6]的有关结果.     

Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique

The main goal of this paper is to introduce and study bilevel vector equilibrium problems. We first establish some existence results for solutions of vector equilibrium problems and mixed vector equilibrium problems. We study the existence of solutions of bilevel vector equilibrium problems by considering a vector Thikhonov-type regularization procedure. By using this regularization procedure and existence results for mixed vector equilibrium problems, we establish some existence results for solutions of bilevel vector equilibrium problems. By using the auxiliary principle, we propose an algorithm for finding the approximate solutions of bilevel vector equilibrium problems. The strong convergence of the proposed algorithm is also studied.     

Existence of positive periodic solutions of nonlinear neutral differential systems with variable delays

In this work we use some mixed techniques of the Mawhin coincidence degree theory and fixed point theorem to prove the existence of positive periodic solutions of delay systems. As a consequence, we offer existence criteria and sufficient conditions for existence of periodic solutions to the systems with feedback control. When these results are applied to some special delay bio-mathematics models, some new results are obtained, and many known results are improved.     

Existence of solutions for sub-linear or super-linear operator equations

We investigate solutions to superlinear or sublinear operator equations and obtain some abstract existence results by minimax methods. These results apply to superlinear or sublinear Hamiltonian systems satisfying several boundary value conditions including Sturm-Liouville boundary value conditions and generalized periodic boundary value conditions, and yield some new theorems concerning existence of solutions or nontrivial solutions. In particular, some famous results about periodic solutions to superlinear or sublinear Hamiltonian systems by Rabinowitz or Benci and Rabinowitz are special cases of the theorems.     

脉冲三点边值问题的变号解

本文首先使用拓扑度和不动点指数方法,得到了关于抽象空间中算子方程变号解及多个变号解存在的几个结果,然后将所得结果应用于一类含脉冲三点边值问题,得到了变号解及多个变号解的存在性结果.     

ALMOST PERIODIC SOLUTIONS OF SINGLE POPULATION MODELS WITH ALMOST PERIODIC ENVIRONMENT

ＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＳＩＮＧＬＥＰＯＰＵＬＡＴＩＯＮＭＯＤＥＬＳＷＩＴＨＡＬＭＯＳＴＰＥＲＩＯＤＩＣＥＮＶＩＲＯＮＭＥＮＴＨｅＣｈｏｎｇｙｏｕ（ＮａｎｊｉｎｇＵｎｉｖｅｒｓｔｙ）（何崇佑）南京大学，邮编：２１０００８Ａｂ...     

POSITIVE SOLUTIONS TO SINGULAR SECOND ORDER PERIODIC BOUNDARY VALUE PROBLEM WITH SIGN-CHANGING NONLINEARITIES

This paper deals with the existence of positive solutions to the singular secondorder periodic boundary value problem. We obtain the existence results of positive solutions by the fixed point index theory. The results obtained extend and complement some known results.