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 $λ$ varies. We also show the existence of minimal positive solutions $u_λ^*$ and determine the monotonicity and continuity properties of the map $λ\mapsto u_λ^*$.

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