Existence and regularity of positive solutions of quasilinear elliptic problems with singular semilinear term

Abstract

This paper deals with existence and regularity of positive solutions of singular elliptic problems on a smooth bounded domain with Dirichlet boundary conditions involving the $\Phi$-Laplacian operator. The proof of existence is based on a variant of the generalized Galerkin method that we developed inspired on ideas by Browder and a comparison principle. By using a kind of Moser iteration scheme we show $L^{\infty }(\Omega )$-regularity for positive solutions