兰州大学机构库 >数学与统计学院
无界区域上p(x)-Lapace方程正解的存在性
Alternative TitleExistence of positive solutions for p(x)-Laplacian equations in unbounded domains
刘舞龙
Thesis Advisor赵培浩
2008-05-26
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keywordp(x)-Lapace方程 (PS)-序列 基态解 高能解
Abstract本文研究如下 -Lapace方程在一定条件下弱解的存在性: 本文遇到的主要困难是无界区域上Sobolev空间缺乏紧性,从而 -条件不成立.为了克服这些困难,本文证明了集中紧性,通过分析 -序列,应用它们的收敛性去判断与方程相对应的能量泛函的临界点的存在性.本文主要的工具有Ekeland变分原理、Nehari流形、集中紧性和变指数Sobolev空间嵌入理论等.通过考虑区域的几何性质和拓扑性质对解的存在性的影响,我们得到当区域满足不同的条件时,方程分别有一个解、一个基态解、一个基态解和一个高能解.
Other AbstractIn this paper we are concerned with the existence of weak solutions of the following -Laplace equations under some conditions. Because of the lack of compactness for the Sobolev space on unbounded domain and then -condition fails, the above problem become more complex. To overcome this difficulty, we prove the compactness of concentration, and analyze -sequence, and use their convergence to ensure the existence of critical points for the corresponding functional. The tools we used here are Ekeland Variational Principle, Nehari manifold, compactness of concentration, imbedding theory of generalized Lebesgue-Sobolev spaces and so on. The existence is affected by the properties of the geometry and the topology of the domain. The problem has a weak solution, has one ground state solution, have a ground state solution and a higher energy solution respectively when the domain satisfy different conditions .
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224591
Collection数学与统计学院
Recommended Citation
GB/T 7714
刘舞龙. 无界区域上p(x)-Lapace方程正解的存在性[D]. 兰州. 兰州大学,2008.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Altmetrics Score
Google Scholar
Similar articles in Google Scholar
[刘舞龙]'s Articles
Baidu academic
Similar articles in Baidu academic
[刘舞龙]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[刘舞龙]'s Articles
Terms of Use
No data!
Social Bookmark/Share
No comment.
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.