关键词: 基态解, 集中性态, 椭圆方程, 集中紧原理

Abstract:
\noindent{\bf Abstract:} The main purpose of this paper is to
analyze the concentration behavior of the ground state solutions
for fourth order equation $\Delta ^2u=|x|^\alpha u^{p-1}$ in
$\Omega $, $u=\Delta u=0$ on $\partial \Omega$~ ($\Omega \subset
R^n$ is a ball centered at the origin). It is proved that for $p$
close to $2^*=\frac{2n}{n-4} (n>4)$, the ground state solution
$u_p$ concentrates near the boundary of $\Omega$.

Key words: Concentration behavior, Elliptic equation, Concentration compactness principle