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 $\Omega$.