Asymptotic behavior of ground state solution for Henon type systems

• Main Authors: Ying Wang, Jianfu Yang
• Format: Article
• Language: English
• Published: Texas State University 2010-08-01
• Series: Electronic Journal of Differential Equations
• Subjects: Asymptotic behavior; Henon systems; ground state solution
• Online Access: http://ejde.math.txstate.edu/Volumes/2010/116/abstr.html

In this article, we investigate the asymptotic behavior of positive ground state solutions, as $alphaoinfty$, for the following Henon type system $$ -Delta u=frac{2p}{p+q}|x|^alpha u^{p-1}v^q,quad -Delta v=frac{2q}{p+q}|x|^alpha u^pv^{q-1},quad hbox{in } B_1(0) $$ with zero boundary condition, where $B_1(0)subsetmathbb{R}^N$ ($Ngeq3$) is the unit ball centered at the origin, $p,q>1$, $p+q<2^*=2N/(N-2)$. We show that both components of the ground solution pair $(u, v)$ concentrate on the same point on the boundary $partial B_1(0)$ as $alphaoinfty$.