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Harmonic functions with nonlinear Neumann boundary condition and their Morse indices
Journal article   Peer reviewed

Harmonic functions with nonlinear Neumann boundary condition and their Morse indices

Mohamed Ben Ayed, Habib Fourti and Abdelbaki Selmi
Nonlinear analysis: real world applications, Vol.38, pp.96-112
12/2017
DOI: https://doi.org/10.1016/j.nonrwa.2017.04.012

Abstract

Blow up analysis Elliptic equation Harmonic function Liouville type theorem Morse index
We consider the solutions of a nonlinear Neumann elliptic equation Δu=0 in Ω, ∂u/∂ν=f(x,u) on ∂Ω, where Ω is a bounded open smooth domain in RN, N≥2 and f satisfies super-linear and subcritical growth conditions. We prove that L∞-bounds on solutions are equivalent to bounds on their Morse indices.

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