Positive Solutions for Anisotropic Singular Dirichlet Problems

We 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 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.

Automated summary

The above study proves a bifurcation-type result on the Dirichlet problem, describing the changes in the set of positive solutions as the parameter varies.