零扰动下一类RN 上临界增长的椭圆方程正解的存在性

本文讨论了N维欧氏空间R~N上一类临界增长的拟线性椭圆型方程—div(|Du|~(p-2)Du)+k(x)u~)p-1)=K(x)U~(p-1),u∈W~(1,p)(R~N)∩L~p(R~N)的正解的存在性。其中4≤p~2≤N,p=Np/(N—p)。在微分几何与物理学等领域起重要作用的Yamabe问题就是其特例(p=2)。本文运用集中紧引理,证明了问题的正解的存在性。

The Exisitence of Positive Solutions of a Quasilinear Elliptic Equation on RN of Critical Increase with Zero-perturbation

This Paper is concerned with the existence of positive solutions. The Yamabe problem which is very important in the fields of differential geometry,physics ,etc is a special example. In this paper,the author has obtained the existence of positive solutions of the above problem by applying the concentrain-compactness lemmas.