一类有Hardy-Sobolev临界指数的椭圆方程的多解性  

Multiplicity of solutions for elliptic problems with critical Hardy-Sobolev exponents

作　　者：谢华朝[1] 李素丽[2] 皮慧荣[1] 

机构地区：[1]华中师范大学数学与统计学学院,武汉430079 [2]空军第一航空学院基础部数学教研室,河南信阳464000

出　　处：《华中师范大学学报（自然科学版）》2008年第2期171-174,共4页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金资助项目(10471052).

摘　　要：证明了具有Hardy-Sobolev临界指数的半线性椭圆方程(1)的解的情况,存在λ*>0,当λ∈(0,λ*)时,运用对偶喷泉定理得方程有无穷多解,且该解序列具有负的能量值;当λ→0+时,解的模趋于零;当λ≤0时,方程没有负能量的解.This paper is a contribution on a semilinear elliptic equation with critical Sobolev and Hardy exponents. With the aids of Dual fountain theorem, it can be obtained that this problem has many solutions with negative energy as λ∈（0,λ^＊）, and the norm of the solutions behave near 0 asymptotically as λ→0^＋ ; for λ≤0, there is no solution with negative energy.

关 键 词：HARDY-SOBOLEV临界指数 (PS)c^＊条件 对偶喷泉定理 多解 

分 类 号：O175.2[理学—数学]