四阶常微分方程边值问题结点解的研究

兰州大学机构库 >数学与统计学院

	四阶常微分方程边值问题结点解的研究
Alternative Title	Nodal solutions for Boundary Value Problems of four-order Ordinary Differential Equations
	沈文国
Thesis Advisor	钟承奎
	2012-05-19
Degree Grantor	兰州大学
Place of Conferral	兰州
Degree Name	博士
Keyword	四阶两点边值问题结点解全局结构多解性正解全局分歧理论锥上不动点理论
Abstract	本学位论文运用Disconjugate理论建立了四阶两点线性特征值问题的谱结果, 在上述谱结果的基础上, 运用分歧理论研究了几类含参非线性四阶两点边值问题结点解、正解的存在性及解的全局结构. 另外, 运用锥上不动点理论还研究了带非齐次边界条件的四阶两点边值问题正解的存在性及解对参数的依赖性. 全文共分六章. 第一章介绍了本文的研究背景及要研究的主要问题,陈述了本文的主要结果及分歧理论的一些预备知识. 第二章证明了含参的四阶线性微分算子满足, 进而建立了一类线性特征值问题谱结果. 当时, 在上述谱结果的基础上, 运用Rabinowitz 全局分歧定理获得了一类四阶两点边值问题结点解的存在性、多解性及解的全局结构. 第四章当,时, 运用Rabinowitz 全局分歧定理和拓扑方法研究并获得了一类四阶两点边值问题结点解的存在性、多解性及全局结构. 第五章当，不存在时,运用区间分歧定理研究并获得了形式更广泛的四阶两点边值问题正解的存在性及解的全局结构. 第六章运用锥上不动点理论研究了一类带非齐次边界条件的四阶两点边值问题正解的存在性及解对参数的依赖性.
Other Abstract	In this doctoral dissertation, we firstly obtain the results of spectrum of a class linear eigenvalue problem. In the following, we gain the global structure of nodal solutions of some problems. In addition, we also study the existence of positive solutions to the nonhomogeneous problem . This thesis consists of six chapters. In chapter one, the background and some preliminaries are introduced. The main problems and the corresponding results are also presented. In chapter two, we obtain the results of spectrum of a class generalized eigenvalue problem . In chapter three, we obtain the global structure and the existence and multiplicity of nodal solutions of a class boundary value problem. Chapter four, we study the global structure and the existence and multiplicity of nodal solutions of a class boundary value problem. In fifth chapter, we obtain global structures of positive solutions for a class boundary value problem. In chapter six, we study the existence of positive solutions to a class nonhomogeneous boundary value problem..
URL	查看原文
Language	中文
Document Type	学位论文
Identifier	https://ir.lzu.edu.cn/handle/262010/224673
Collection	数学与统计学院
Recommended Citation GB/T 7714	沈文国. 四阶常微分方程边值问题结点解的研究[D]. 兰州. 兰州大学,2012.

Files in This Item:
There are no files associated with this item.

If you have any objections to this item, please fill out the form below and the administrator will contact you as soon as possible.
Content:
Email：	*
Institution:
Verification Code:	Refresh

Any comments and suggestions are welcomed.
Title:	*
Content:
Email：	*
Verification Code:	Refresh

数学与统计学院知识库