Anisotropic Singular Neumann Equations with Unbalanced Growth

We consider a nonlinear parametric Neumann problem driven by the anisotropic (p, q)-Laplacian and a reaction which exhibits the combined effects of a singular term and of a parametric superlinear perturbation. We are looking for positive solutions. Using a combination of topological and variational tools together with suitable truncation and comparison techniques, we prove a bifurcation-type result describing the set of positive solutions as the positive parameter lambda varies. We also show the existence of minimal positive solutions u(lambda)* and determine the monotonicity and continuity properties of the map lambda bar right arrow u(lambda)*.

Automated summary

The article investigates a nonlinear parametric Neumann problem driven by the anisotropic (p, q)-Laplacian with a singular term and parametric superlinear perturbation, seeking positive solutions. By using a combination of topological and variational tools, the study proves a bifurcation-type result describing the set of positive solutions as the positive parameter lambda varies. The existence of minimal positive solutions u(lambda)* is also shown, along with determining the monotonicity and continuity properties of the map lambda bar right arrow u(lambda)*.