Geodesic
Ground state solutions for semilinear problems with a Sobolev-Hardy term
Electronic Journal of Differential Equations, Tome 2013 (2013).

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

Summary: In this article, we study the existence of solutions to the problem $$\displaylines{ -\Delta u= \lambda u+\frac{|u|^{2_s^\ast-2}u}{|y|^s}, \quad x\in \Omega,\cr u = 0, \quad x\in \partial \Omega, }$$ where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N(N\geq3)$. We show that there is a ground state solution provided that N=4 and $\lambda_m\lambda\lambda_{m+1}$, or that $N\geq 5$ and $\lambda_m\leq\lambda\lambda_{m+1}$, where $\lambda_m$ is the m'th eigenvalue of $-\Delta$ with Dirichlet boundary conditions.
Classification : 35J60, 35J65
Keywords: existence, ground state, critical Hardy-Sobolev exponent, semilinear Dirichlet problem 
@article{EJDE_2013__2013__a181,
     author = {Chen, Xiaoli and Chen, Weiyang},
     title = {Ground state solutions for semilinear problems with a {Sobolev-Hardy} term},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a181/}
}
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Chen, Xiaoli; Chen, Weiyang. Ground state solutions for semilinear problems with a Sobolev-Hardy term. Electronic Journal of Differential Equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a181/