Singular p-Laplacian equations with superlinear perturbation

Abstract

We consider a nonlinear Dirichlet problem driven by the p-Laplace operator and with a right-hand side which has a singular term and a parametric superlinear perturbation. We are interested in positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter λ>0 varies. In addition, we show that for every admissible parameter λ>0 the problem has a smallest positive solution u‾λ and we establish the monotonicity and continuity properties of the map λ→u‾λ.