几类非线性方程解的存在及其应用

【作者】 姜燕君；

【导师】 刘立山；

【作者基本信息】 曲阜师范大学 ， 应用数学， 2005， 硕士

【摘要】 非线性泛函分析是现代分析数学的一个重要分支,因其能很好的解释自然界中的各种各样的自然现象从而受到了越来越多的数学工作者的关注。其中,非线性脉冲问题和奇异边值问题来源于应用数学和物理的多个分支,是目前分析数学中研究较为活跃的领域。根据内容我们将本文分成了四章。 在第一章中,我们给出了绪论。 在第二章的第一节里,我们利用M(?)nch不动点定理和比较结果,研究了实Banach空间中一阶非线性脉冲微分-积分方程初值问题解的存在性; 第二章第二节,我们在没有任何紧型条件而且只有一个上解或者下解的假设下研究了下面方程解的存在性: 第三章我们利用新的比较结果和M(?)nqh不动点定理,研究了实Banach空间中二阶混合型脉冲微分-积分方程两点边值问题整体解的存在性:更多还原

【Abstract】 Nonlinear functional analysis is an important branch of modern analysis mathematics, because it can explain all kinds of natural phenomenon, more and more mathematicans are spending their time on it. Among them, the nonlinear impulsive problems and singular boundary problems arise from a lot of branches of applied mathematics and physics, which are at present active fields in analysis mathematics. The paper is divided into four chapters according to the contents.In the first chapter, we give the preface.In the first section of Chapter Two, by using the Monch fixed point theorem and a comparison result, we shall study the existence theorems of solutions of intial value problem for the first order nonlinear impulsive integro-differential equations :In the second section of Chapter Two, we study the existence of a unique solution of the following equation under the hypothesis that the equation does not satisfy any compactness-type conditions and has only an upper (or a lower)solution:In the third chapter, we exploit a new comparison result and the Monch fixed point theorem to prove the existence theorem of global solutions for two-point boundary value problems of second order impulsive integro-differential equations in Banach spaces:更多还原