【作者】 张海燕；

【导师】 陈芳启；

【作者基本信息】 天津大学 ， 应用数学， 2004， 硕士

【摘要】 本文研究的主要是关于Banach空间中二阶非线性脉冲积分-微分方程的初值问题和边值问题。特别地,讨论了对于同一类型的方程在不同的初值和边值的条件下解的存在性。本文分为三部分。 在第一章中,主要介绍线性泛函和非线性泛函中与本文相关的一些基本概念、术语、性质和定理。为后两部分做初步的介绍并为全文打下基础。 在第二章中,利用比较结果、等价范数、Banach不动点定理和单调迭代方法,得到Banach空间中二阶非线性脉冲积分-微分方程初值问题的最大最小解的一个充分条件,建立了解的存在定理。并且,利用非紧性测度得到最大最小解的另一个充分条件。同时,在较弱的条件下,利用Gronwall不等式建立解的存在定理。 本文的第三章,主要解决了Banach空间中二阶非线性脉冲积分-微分方程三点边值问题。对于两类具有一端点值固定的两种不同的边界条件来寻找不同的先验估计,获得了两类二阶三点边值问题解的存在性,并利用Leray-Schauder不动点定理建立解的存在定理。更多还原

【Abstract】 The present dissertation is devoted to initial value problems and boundary value problems for second order impulsive integro-differential equations in Banach spaces. Especially, when the initial conditions are different, we study the existence of solutions and establish the existence theorems of solutions. This paper is mainly divided into three chapters.In the first chapter, we introduce some important concepts, notations, auxiliary results and accept certain basic principles of linear functional analysis and nonlinear functional analysis, which are quoted here for easier references until they are applied in later chapters.In the second chapter, by established comparison results, through introducing the equivalent norm , by applying Banach fixed theorem and using the monotone iterative technique, we obtain one sufficient condition of existence of maximal and minimal solutions to initial value problem for second order impulsive integro-differential equation in Banach spaces. And we give another sufficient condition of existence of maximal and minimal solutions based on the Kuratowski measure of noncompactness. At the same time, under weaker conditions, we establish the existence theorems of solutions by using Gronwall inequality.In the third chapter, we investigate three-point boundary value problems for second order impulsive integro-differential equations in Banach spaces. By using different methods, we obtain the different prior estimates with their values fixed at one end point and different boundary conditions. Thus, we establish the existence theorems of solutions by employing Leray-Schauder fixed theorem.更多还原