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

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.

Keywords

• topological approach
• fixed point
• regularity theory
• purely singular problem
• truncation
• 35j20
• 35j75