Document Type

Article

Publication Date

6-1-2017

Published In

Proceedings Of The Royal Society Of Edinburgh Section A: Mathematics

Abstract

We consider reaction–diffusion equations under nonlinear boundary conditions where the nonlinearities are asymptotically linear at infinity and depend on a parameter. We prove that, as the parameter crosses some critical values, a resonance-type phenomenon provides solutions that bifurcate from infinity. We characterize the bifurcated branches when they are sub- or supercritical. We obtain both Landesman–Lazer-type conditions that guarantee the existence of solutions in the resonant case and an anti-maximum principle.

Keywords

Steklov eigenvalues, elliptic equations, nonlinear boundary conditions, Bifurcation

Available for download on Monday, January 01, 2018

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