Geodesic
Existence of solutions for Hardy-Sobolev-Maz'ya systems
Electronic Journal of Differential Equations, Tome 2012 (2012).

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

Summary: The main goal of this article is to investigate the existence of solutions for the Hardy-Sobolev-Maz'ya system $$\displaylines{ -\Delta u-\lambda \frac{u}{|y|^2}=\frac{|v|^{p_t-1}}{|y|^t}v,\quad \hbox{in }\Omega,\cr -\Delta v-\lambda \frac{v}{|y|^2}=\frac{|u|^{p_s-1}}{|y|^s}u,\quad \hbox{in }\Omega,\cr u=v=0,\quad \hbox{on }\partial \Omega }$$ where $0\in\Omega$ which is a bounded, open and smooth subset of $\mathbb{R}^k\times \mathbb{R}^{N-k}, 2\leq k$. The non-existence of classical positive solutions is obtained by a variational identity and the existence result by a linking theorem.
Classification : 35J47, 35J50, 35J57, 58E05
Keywords: variational identity, (PS) condition, linking theorem, Hardy-Sobolev-maz'ya inequality 
@article{EJDE_2012__2012__a40,
     author = {Wang, Jian and Wei, Xin},
     title = {Existence of solutions for {Hardy-Sobolev-Maz'ya} systems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a40/}
}
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Wang, Jian; Wei, Xin. Existence of solutions for Hardy-Sobolev-Maz'ya systems. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a40/