Geodesic
Asymptotic behavior of ground state solution for Hénon type systems
Electronic Journal of Differential Equations, Tome 2010 (2010).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2010},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a17/}
}
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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/