Geodesic
Three solutions for singular $p$-Laplacian type equations
Electronic Journal of Differential Equations, Tome 2008 (2008).

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

Summary: In this paper, we consider the singular $$\displaylines{ -\hbox{div}(|x|^{-\beta} a(x,\nabla u)) =\lambda f(x,u),\quad \hbox{in }\Omega,\cr u=0,\quad \hbox{on }\partial\Omega, }$$ where $0\leq\beta$ is a smooth bounded domain in $\mathbb{R}^N$ containing the origin, $f$ satisfies some growth and singularity conditions. Under some mild assumptions on $a$, applying the three critical points theorem developed by Bonanno, we establish the existence of at least three distinct weak solutions to the above problem if $f$ admits some hypotheses on the behavior at $u=0$ or perturbation property.
Classification : 35J60
Keywords: p-Laplacian operator, singularity, multiple solutions 
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     author = {Yang, Zhou and Geng, Di and Yan, Huiwen},
     title = {Three solutions for singular $p${-Laplacian} type equations},
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Yang, Zhou; Geng, Di; Yan, Huiwen. Three solutions for singular $p$-Laplacian type equations. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a59/