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

Abstract

Theexistenceofatleasttwosmoothpositivesolutionsforaparametricquasilinearelliptic 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 minimizes. An explicit quantitative estimate from below of the best theoretically parameters considered is furnished.