含Hardy位势与临界参数的渐近线性椭圆型方程

J4 ›› 2012, Vol. 47 ›› Issue (2): 14-18.

含Hardy位势与临界参数的渐近线性椭圆型方程

王江潮, 张贻民*

中国科学院武汉物理与数学研究所, 湖北武汉 430071

收稿日期:2011-01-06 出版日期:2012-02-20 发布日期:2012-12-24
通讯作者: 张贻民(1980- ), 男,博士后,研究方向为非线性椭圆型方程. Email:zhangym802@126.com
作者简介:王江潮(1985- ),男, 博士生,研究方向为非线性椭圆型方程. Email:rightatyou@gmail.com
基金资助:
国家自然科学基金资助项目(10801132,11001261)

Solutions for asymptotically linear elliptic equations involving Hardy potential and critical parameter

WANG Jiang-chao, ZHANG Yi-min*

Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, Hubei, China

Received:2011-01-06 Online:2012-02-20 Published:2012-12-24

摘要/Abstract

摘要：

考虑一类含Hardy位势与临界参数的渐近线性椭圆型方程。对于一般有界区域Ω, 此类方程在H¹₀(Ω)中不存在非平凡解。本文应用Morse理论, 在新的Sobolev-Hardy空间中得到了非平凡解的存在性。

关键词: Hardy位势；临界参数；渐近线性；Morse理论

Abstract:

A class of asymptotically linear elliptic equations with Hardy potential and critical parameter is considered. For general bounded domain Ω, there is no nontrivial solution in space H¹₀ (Ω) for this kind of equation (see reference［1］). The existence of non-trivial solutions are proved in a new Sobolev-Hardy space with the technique of Morse theory.

Key words: Hardy potential; critical parameter; asymptotically linear; Morse theory

王江潮, 张贻民*. 含Hardy位势与临界参数的渐近线性椭圆型方程[J]. J4, 2012, 47(2): 14-18.

WANG Jiang-chao, ZHANG Yi-min*. Solutions for asymptotically linear elliptic equations involving Hardy potential and critical parameter[J]. J4, 2012, 47(2): 14-18.

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