兰州大学机构库 >数学与统计学院
两类奇异椭圆方程解的存在性
Alternative TitleExistence of Solutions for Two Classes of Singular Elliptic Equations
柳彦军
Thesis Advisor赵培浩
2014-05-28
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword指数次临界增长 奇异Trudinger-Moser型不等式 山路引理 Vitali 收敛定理 集中紧性原理
Abstract本文考虑两类奇异椭圆方程解的存在性. 首先, 考虑Trudinger-Moser型奇异椭圆问题, 在合适的函数空间给出此类问题解的合理定义, 使用山路引理与Vitali收敛定理得到了该问题基态解的存在性. 更进一步, 在无A-R条件时得到了类似的结果. 其次, 考虑一类奇异非线性椭圆方程的Dirichlet问题, 利用P. L. Lions的集中紧性原理, 对这类包含奇异项与临界项的非线性椭圆问题得到了正的弱解.
Other AbstractIn this paper, we consider the existence of solutions for two classes of singular elliptic equations. First, we consider Trudinger-Moser elliptic problem and give the reasonable definition of solution in suitable function space. we get the existence of ground state solution for elliptic problem by using Mountain-pass theorem and Vitali convergence theorem. Furthermore, we get a similar result without A-R condition. Second, we consider a singular Dirichlet problem to nonlinear elliptic equation, By means of the concentration compactness principle due to P. L. Lions, the positive weak solution is obtained for the class of nonlinear elliptic problem containing both singular and critical terms.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224885
Collection数学与统计学院
Recommended Citation
GB/T 7714
柳彦军. 两类奇异椭圆方程解的存在性[D]. 兰州. 兰州大学,2014.
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