Geodesic
Asymptotic behavior of ground state solution for Hénon type systems
Electronic journal of differential equations, Tome 2010 (2010)
In this article, we investigate the asymptotic behavior of positive ground state solutions, as

$ -\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 $B_1(0)\subset\mathbb{R}^N (N\geq3)$ is the unit ball centered at the origin, $p,q>1, p+q2^*=2N/(N-2)$. 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 $\alpha\to\infty$.
Classification : 35J50, 35J57, 35J47
Keywords: asymptotic behavior, henon systems, ground state solution 
@article{EJDE_2010__2010__a17,
     author = {Wang,  Ying and Yang,  Jianfu},
     title = {Asymptotic behavior of ground state solution for {H\'enon} type systems},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1198.35084},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a17/}
}
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JO  - Electronic journal of differential equations
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%A Yang,  Jianfu
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%J Electronic journal of differential equations
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%V 2010
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%F EJDE_2010__2010__a17
Wang,  Ying; Yang,  Jianfu. Asymptotic behavior of ground state solution for Hénon type systems. Electronic journal of differential equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a17/