Anisotropic singular Neumann equations with unbalanced growth

Abstract

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 $u_{\lambda }^{\ast }$ and determine the monotonicity and continuity properties of the map $\lambda \mapsto u_{\lambda }^{\ast }$.

References in corpus (5)

• Regularity for minimizers for functionals of double phase with variable exponents
• Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves
• Nonlinear nonhomogeneous singular problems
• Ground state and nodal solutions for a class of double phase problems
• Anisotropic equations with indefinite potential and competing nonlinearities