Singular p-Laplacian equations with superlinear perturbation

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 lambda > 0 varies. In addition, we show that for every admissible parameter lambda > 0 the problem has a smallest positive solution (u) over bar (lambda) and we establish the monotonicity and continuity properties of the map lambda -> (u) over bar (lambda). (C) 2018 Elsevier Inc. All rights reserved.