含有Sobolev-Hardy临界指数的拟线性椭圆方程解的存在性和多重性  

EXISTENCE AND MULTIPLICITY RESULTS FOR SOME QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL SOBOLEV-HARDY EXPONENT

作　　者：龚亚英[1] 

机构地区：[1]重庆三峡职业学院基础部

出　　处：《数学杂志》2009年第4期500-504,共5页Journal of Mathematics

摘　　要：本文研究了一类含有Sobolev-Hardy临界指数的拟线性奇异椭圆方程解的存在性和多重性.利用Ekeland变分原理和Clark临界点定理证明了该问题非平凡解和无穷多解的存在性,推广了已有结果.This paper concerns the existence and multiplicity of solutions for some quasilinear elliptic equation with critical Sobolev-Hardy exponent. By using Ekeland;s variational principle, we conclude the existence of nontrivial solution for this problem. The Clark＇s critical point theorem is used to prove the existence of infinitely many solutions for this problem with odd nonlinearity.

关 键 词：SOBOLEV-HARDY临界指数 拟线性椭圆方程 亏格 Brezis—Lieb引理 

分 类 号：O175.25[理学—数学]