1. National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece;2. Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany
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 varies. In addition, we show that for every admissible parameter the problem has a smallest positive solution and we establish the monotonicity and continuity properties of the map .