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 C1 versus Sobolev minimizers. An explicit quantitative estimate from below of the best theoretical parameters considered is furnished.