含Hardy位势与临界参数的渐近线性椭圆型方程

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

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。

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.