Positive solutions for nonlinear parametric singular Dirichlet problems

Abstract

We consider a nonlinear parametric Dirichlet problem driven by the [Formula: see text]-Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Carathéodory perturbation which is ([Formula: see text])-linear near [Formula: see text]. The problem is uniformly nonresonant with respect to the principal eigenvalue of [Formula: see text]. We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter [Formula: see text].