Singular Dirichlet $(p,q)$-equations

Nikolaos S. Papageorgiou; Patrick Winkert

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arXiv · 2003.07601

Singular Dirichlet $(p,q)$-equations

Nikolaos S. Papageorgiou·Patrick Winkert

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Abstract

We consider a nonlinear Dirichlet problem driven by the $(p,q)$-Laplacian and with a reaction having the combined effects of a singular term and of a parametric $(p-1)$-superlinear perturbation. We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter $λ>0$ varies. Moreover, we prove the existence of a minimal positive solution $u^*_λ$ and study the monotonicity and continuity properties of the map $λ\to u^*_λ$.

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BibTeX RIS

Nikolaos S. Papageorgiou, Patrick Winkert. 2021-04-23. Singular Dirichlet $(p,q)$-equations. https://arxiv.org/abs/2003.07601

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