Nonlinear singular problems with convection

Abstract

In this paper we study the existence of a positive solution for a nonlinear Dirichlet problem driven by the p -Laplacian and a reaction which has the competing effects of a singular term and of a convection (gradient dependent) term. Using the “frozen” variable method and eventually the Leray-Schauder Alternative Theorem, we show that the problem has a positive smooth solution. We mention that on the gradient dependent perturbation x ↦ f ( z , x , y ) , we do not impose any bilateral growth condition.