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 TitleNodal 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 AbstractIn 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
Identifierhttps://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.
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