论文摘要
本文利用变分法主要研究了分数阶Laplacian问题解的存在性与多解性,其中首先研究了非局部临界问题.假设非线性项满足一定的增长性条件,利用山路引理和环绕定理可分别得到临界问题单个解的存在性,这个结果推广了Servadei等人[Trans.Amer.Math.Soc.,2015],[Rev.Mat.Complut.,2015],也包含了[Adv.Nonlinear Anal.,2013]的定理1.1.更重要的是,本文证明了临界问题多个解的存在性,此结果是Sang[Nonlinear Anal.,1994],Fiscella等人[Bull.Sci.Math.,2016]主要结果的推广.随后,本文还研究了非局部次临界问题.当非线性项满足合适的增长性条件时,通过对称山路引理,得到次临界问题存在无穷多个解.这个结果推广了Kajikiya等人[J.Math.Anal.Appl.,1990],Zhang等人[Nonlinearity.,2015]的主要结果。
论文目录
文章来源
类型: 硕士论文
作者: 李盼丽
导师: 孙红蕊
关键词: 非局部算子,临界点理论,变分法,存在性,多解性
来源: 兰州大学
年度: 2019
分类: 基础科学
专业: 数学
单位: 兰州大学
分类号: O175
总页数: 46
文件大小: 1878K
下载量: 35
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