四阶椭圆方程基态解的集中性态  

Concentration Behavior of the Ground State Solutions for Fourth Order Elliptic Equation

作　　者：罗琳[1] 徐国进[1] 

机构地区：[1]孝感学院数学系,孝感432100

出　　处：《数学物理学报（A辑）》2007年第4期761-768,共8页Acta Mathematica Scientia

基　　金：湖北省教育厅研究项目(2004D004)资助

摘　　要：该文分析了四阶椭圆方程Δ~2u=|x|~αu^(p-1),x∈Ω;u=Δu=0,x∈■Ω,(Ω表示R^n中以原点为中心的球)基态解的集中性态,并证明了当p趋近于2~*=(2_n/n-4)(n>4)时基态解u_p集中在Ω的边界附近.The main purpose of this paper is to analyze the concentration behavior of the ground state solutions for fourth order equation Δ^%2u=｜x｜^αu^（p-1）,x∈Ω;u=Δu=0,x∈δΩ,（Ω belong to Rn is a all centered at the origin）. It is proved that for p close to2^＊=（2n/n-4）（n〉4）, the ground state solution up concentrates near the boundary of Ω.

关 键 词：基态解 集中性态 椭圆方程 集中紧原理 

分 类 号：O175.25[理学—数学]