论文摘要
本文主要研究一类带p-Laplkcian算子的四阶微分方程边值问题的正解的存在性和一类带p（t）-Laplacian算子的多点边值问题解的存在性.文章首先运用范数形式的锥拉伸与锥压缩不动点定理讨论一类四阶微分方程边值问题的正解存在性,给出系统至少存在一个或两个正解的充分条件;然后运用Leray-Schauder度方法和不动点定理研究在给定的条件下带p（t）-Laplacian算子的多点边值问题解的存在性.全文的结构如下:第一章主要介绍本文的研究背景、研究内容和本文的主要工作,以及在下面章节中将会用到的p-Laplacian算子的相关知识以及一些不动点定理.第二章主要运用锥拉伸与锥压缩不动点定理研究一类带p-Laplacian算子的四阶微分方程边值问题解的存在性:证明该方程至少存在一个或者两个正解且正解与参数λ有关,其中λ>0.然后给出对应的例子来说明定理的可行性.第三章主要运用Leray-S chauder度方法及不动点定理研究一类带p（t）-Laplacian算子的多点边值问题解的存在性,本章给出两个可用于判定这类带p（t）-Laplacian算子的多点边值问题是否存在解的充分条件,并给出对应的例子.
论文目录
文章来源
类型: 硕士论文
作者: 梁锦芳
导师: 罗治国
关键词: 四阶微分方程边值问题,解的存在性,不动点定理,度理论
来源: 湖南师范大学
年度: 2019
分类: 基础科学
专业: 数学
单位: 湖南师范大学
分类号: O175.8
总页数: 49
文件大小: 1515K
下载量: 23
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标签：四阶微分方程边值问题论文; 解的存在性论文; 不动点定理论文; 度理论论文;