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arXiv · 2010.00269

Robin double-phase problems with singular and superlinear terms

Nikolaos S. Papageorgiou·Vicenţiu D. Rădulescu·Dušan D. Repovš
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Abstract

We consider a nonlinear Robin problem driven by the sum of $p$-Laplacian and $q$-Laplacian (i.e. the $(p,q)$-equation). In the reaction there are competing effects of a singular term and a parametric perturbation $λf(z,x)$, which is Carathéodory and $(p-1)$-superlinear at $x\in\mathbb{R},$ without satisfying the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques, we prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter $λ>0$ varies.

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Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. 2020-10-01. Robin double-phase problems with singular and superlinear terms. https://doi.org/10.1016/j.nonrwa.2020.103217

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