THE PERTURBATION PROBLEM OF AN ELLIPTIC SYSTEM WITH SOBOLEV CRITICAL GROWTH  

作　　者：Qi LI 李奇(School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China)

机构地区：[1]School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China

出　　处：《Acta Mathematica Scientia》2020年第5期1391-1404,共14页数学物理学报（B辑英文版）

基　　金：supported by the excellent doctorial dissertation cultivation grant(2018YBZZ067 and 2019YBZZ057)from Central China Normal University.

摘　　要：In this paper,we study the following perturbation problem with Sobolev critical exponen t:{-Δu=(1+εK(x))u^2*-1+α/2*u^a-1v^3+εh(x)u^pP,x∈R^N,-Δu=(1+εQ(x))v^2*-1+β/2*u^B-1+εl(x)u^q,x∈R^N,u>0,v>0,x∈R^N where 0<p,q<1,α+β=2*:=2N/N-2,α,β≥3,4.Using a perturbation argument and a finite dimensional reduc tion met hod,we get the exis tence of positive solutions to problem(0.1)and the asymptotic property of the solutions.

关 键 词：perturbation argument finite dimensional reduction method critical exponent 

分 类 号：O175.25[理学—数学]