数学专业硕士论文代写《论非连续增算子的不动点定理以及其应用》
【摘要】 本文给出了Banach空间的一个增算子不动点定理,并将这一定理应用到Banach空间含间断项的二阶非线性脉冲积-微分方程,得到了一类积-微分方程的最大解与最小解的存在性定理.本硕士论文共分为五章.第一章主要介绍了增算子及脉冲积-微分方程理论的发展背景和最新动向,分析了国内一些专家学者在增算子不动点问题的研究中所取得的相关成果.第二章在较弱的伪可分条件下证明了Banach空间上的非连续增算子的不动点定理.特别地,获得了最大不动点与最小不动点的存在性,改进了已有的某些结果.第三、四章的内容是作为对不动点定理的应用,给出了适用于一类积-微分方程的最大解和最小解的存在性定理,并讨论了Banach空间含间断项的二阶非线性脉冲积-微分方程的初值问题和周期边值问题.通过建立比较定理,从讨论含间断项的二阶线性脉冲积-微分方程解的存在唯一性入手,应用不动点定理与上、下解方法证明了含间断项的二阶非线性脉冲积-微分方程的最大解与最小解的存在性,推广了某些文献中的相应结果.最后,在第五章部分总结了本文所做的工作,并对未来工作的研究方向作了展望. 更多还原
硕士论文代写-【Abstract】 In this paper, a new fixed point theorem for discontinuous increasing operators in Banac-h Spaces is obtained. Applying it to the second order discontinuous nonlinear impulsive integro-differential equations in Banach spaces, the result about the existence of its maximal and minimal solutions for a class of integro-differential equations is given.This paper is mainly divided into five chapters.In chapter one, the developments of increasing operators and impulsive integro-differen-tial theory and the latest results are introduced, then some results of maximal and minimal fixed points problems are studied, which are given by some experts in the inner country.In chapter two, the maximal and minimal fixed points theorems for a class of discontinu-ous increasing operators in Banach spaces are proved under weaker pseudo-separable conditi-ons, and some well-known results are improved.In chapter three and four, as applications, the result about the existence of its maximal and minimal solutions for a class of integro-differential equations is given, the initial value problems and periodic boundary value problems for second order discontinuous nonlinear impulsive integro-differential equations in Banach spaces are investigated. By establishing comparison theorems, investigating the existence and uniqueness of solutions of the second order discontinuous linear impulsive integro-differential equations in Banach spaces, using a fixed point theorem and upper and lower solutions method, the existence of maximal and mi-nimal solutions of the second order discontinuous nonlinear impulsive integro-differential equations in Banach spaces is proved. The corresponding results in some well-known papers are generalized and improved.Finally, in chapter five, the work of the paper is aggregated and the future work of the re-search is discussed.
【关键词】 增算子； 不动点； 上下解方法； 初值问题； 周期边值问题；
【Key words】 increasing operators； maximal and minimal fixed points； upper and lower soluteons method； initial value problem； periodic boundary value problem；//