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arXiv · 2205.09535

Anisotropic singular Neumann equations with unbalanced growth

Nikolaos S. Papageorgiou·Vicenţiu D. Rădulescu·Dušan D. Repovš
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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 $u_\lambda^*$ and determine the monotonicity and continuity properties of the map $\lambda\mapsto u_\lambda^*$.

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Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. 2022-05-19. Anisotropic singular Neumann equations with unbalanced growth. https://doi.org/10.1007/s11118-021-09905-4

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