(p,q)-Equations with singular and concave convex nonlinearities

Abstract

We consider a nonlinear Dirichlet problem driven by the (p, q)-Laplacian with 1 < q < p. The reaction is parametric and exhibits the competing effects of a singular term and of concave and convex nonlinearities. We are looking for positive solutions and prove a bifurcation-type theorem describing in a precise way the set of positive solutions as the parameter varies. Moreover, we show the existence of a minimal positive solution and we study it as a function of the parameter.