Geodesic
Three solutions for singular \(p\)-Laplacian type equations
Electronic journal of differential equations, Tome 2008 (2008)
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 
@article{EJDE_2008__2008__a59,
     author = {Yang,  Zhou and Geng,  Di and Yan,  Huiwen},
     title = {Three solutions for singular {\(p\)-Laplacian} type equations},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1177.35082},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a59/}
}
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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/