Positive Solutions for Anisotropic Singular Dirichlet Problems

Abstract

AbstractWe consider a Dirichlet problem driven by a (p(z), q(z))-Laplacian and a reaction involving the sum of a parametric singular term plus a superlinear perturbation. We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter $$\lambda >0$$ λ > 0 varies. Also we show that for every admissible parameter the problem has a smallest positive solution and obtain the monotonicity and continuity properties of the minimal solution map.