Singular Dirichlet (p,q)-equations

2020/03/17 by Papageorgiou, Nikolaos S., Winkert, Patrick
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.07601

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→ u^*_λ.

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