Positive solutions for a class of singular (p, q)-equations

Abstract

Abstract We consider a nonlinear singular Dirichlet problem driven by the ( p , q ) \left(p,q) -Laplacian and a reaction where the singular term u − η {u}^{-\eta } is multiplied by a strictly positive Carathéodory function f ( z , u ) f\left(z,u) . By using a topological approach, based on the Leray-Schauder alternative principle, we show the existence of a smooth positive solution.