四阶椭圆方程基态解的集中性态

该文分析了四阶椭圆方程△^２u=|x|^au^p-1,x∈Ω; u=Delta u=0 , x ∈аΩ, (Ω表示Rⁿ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^*=frac{2n}{n-4} (n>4)时基态解u_p集中在Ω的边界附近.

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

noindent{bf Abstract:} The main purpose of this paper is toanalyze the concentration behavior of the ground state solutionsfor fourth order equation $Delta ^2u=|x|^alpha u^{p-1}$ in$Omega $, $u=Delta u=0$ on $partial Omega$~ ($Omega subsetR^n$ 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 $Omega$.