About positive $W_{loc}^{1,\Phi}(\Omega)$-solutions to quasilinear elliptic problems with singular semilinear term
Keywords
$\Phi$-Laplacian, Orlicz--Sobolev spaces, singular, Galerkin methodAbstract
This paper deals with the existence, uniqueness and regularity of positive
$W_{\rom loc}^{1,\Phi}(\Omega)$-solutions of singular elliptic problems on a~smooth bounded domain with Dirichlet boundary conditions involving the $\Phi$-Laplacian operator.
The proof of the existence is based on a variant of the generalized Galerkin method that we developed inspired by ideas of Browder \cite{Browder} and a comparison principle. By the use of a kind of Moser's iteration scheme we show the
$L^{\infty}(\Omega)$-regularity for positive solutions.
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