Hénon方程基态解的集中性态(英文)

THE CONCENTRATION BEHAVIOR OF THE GROUND STATE SOLUTIONS FOR HENON EQUATION

本文主要分析了含原点区域上零边界条件的H啨ｎｏｎ方程 -Δpu =|x|αuq - 1基态解的集中性态 ,证明了当q→p =np/(n -p) ,(n >p >1 )时 。

The main purpose of this paper is to analyze the concentration behaviour of the ground state solution of Hénon equation -Δ pu=|x| αu q-1 in Ω, u =0 on Ω,(Ω R n is a ball centered at the origin). It is proved that for q close to p *=np/(n-p),(n>p>1) , the ground state solution u q concentrates near the boundary of Ω.