Positive solutions for a $p$-Laplacian equation with sub-critical singular parametric reaction term

Abstract

The existence of at least two smooth positive solutions for a parametric quasilinear elliptic problem driven by a $p$-Laplacian operator involving a mildly singular non-linearity perturbed with a sub-critical term is established. Although, to get our conclusions, we combine variational and truncation techniques, we do not use the usual trick of $C^1$ versus Sobolev minimizers. An explicit quantitative estimate from below of the best theoretical parameters considered is furnished.