关于一类带有 Hardy 项与临界 Sobolev-Hardy指数项的椭圆方程的多解性问题的研究

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	关于一类带有 Hardy 项与临界 Sobolev-Hardy指数项的椭圆方程的多解性问题的研究
Alternative Title	On the existence of multiple solutions for a singular elliptic equation involving critical Sobolev-Hardy exponents in R^N
	邓明旺
Thesis Advisor	钟承奎
	2012-05-20
Degree Grantor	兰州大学
Place of Conferral	兰州
Degree Name	硕士
Keyword	集中列紧性原理临界点理论极小极大原理临界Sobolev-Hardy指数奇异椭圆方程
Abstract	在这篇硕士论文中,我们主要研究了一类含有Hardy项以及带有多个临界 Sobolev-Hardy 指数项的半线性椭圆方程在全空间上的多解性问题: 首先运用集中列紧性原理验证(P.S.)_C <下标!>条件,然后根据极小极大方法以及Z_2 <下标!>指标理论,当参数在满足一定的条件时,我们得到该方程有无穷多个解.
Other Abstract	In this master's dissertation , we study the singular elliptic equation involving multi-singular inverse square potentials and critical Sobolev-Hardy exponents and derive the existence of infinitely many solutions. We first prove a slight variant of concentration compactness principle, by means of the principle and minimax principle, and the Z_2<下标!> index theorem, we obtain infinitely many solutions for suitable positive parameters.
URL	查看原文
Language	中文
Document Type	学位论文
Identifier	https://ir.lzu.edu.cn/handle/262010/225329
Collection	数学与统计学院
Recommended Citation GB/T 7714	邓明旺. 关于一类带有 Hardy 项与临界 Sobolev-Hardy指数项的椭圆方程的多解性问题的研究[D]. 兰州. 兰州大学,2012.

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