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arXiv · 2103.07741

Multiplicity for a strongly singular quasilinear problem via bifurcation theory

Carlos Alberto Santos·Jacques Giacomoni·Lais Santos
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Abstract

A $p$-Laplacian elliptic problem in the presence of both strongly singular and $(p-1)$-superlinear nonlinearities is considered. We employ bifurcation theory, approximation techniques and sub-supersolution method to establish the existence of an unbounded branch of positive solutions, which is bounded in positive $\lambda-$direction and bifurcates from infinity at $\lambda=0$. As consequence of the bifurcation result, we determine intervals of existence, nonexistence and, in particular cases, global multiplicity.

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Carlos Alberto Santos, Jacques Giacomoni, Lais Santos. 2021-03-13. Multiplicity for a strongly singular quasilinear problem via bifurcation theory. https://arxiv.org/abs/2103.07741

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