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arXiv · 1109.5089

A note on the implicit function theorem for quasi-linear eigenvalue problems

Robin Nittka
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Abstract

We consider the quasi-linear eigenvalue problem $-Δ_p u = λg(u)$ subject to Dirichlet boundary conditions on a bounded open set $Ω$, where $g$ is a locally Lipschitz continuous functions. Imposing no further conditions on $Ω$ or $g$ we show that for small $λ$ the problem has a bounded solution which is unique in the class of all small solutions. Moreover, this curve of solutions depends continuously on $λ$.

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Robin Nittka. 2011-09-23. A note on the implicit function theorem for quasi-linear eigenvalue problems. https://doi.org/10.1016/j.na.2011.11.023

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