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Bifurcation from infinity for reaction-diffusion equations under nonlinear boundary conditions

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Mavinga, Nsoki and Pardo, Rosa (2017) Bifurcation from infinity for reaction-diffusion equations under nonlinear boundary conditions. Proceedings of the Royal Society of Edinburgh, 147A . pp. 649-671.

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Official URL: https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/bifurcation-from-infinity-for-reactiondiffusion-equations-under-nonlinear-boundary-conditions/F0FE26BE68A49601B048A13B84EFE0D2



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.


Item Type:Article
Uncontrolled Keywords:Steklov eigenvalues; elliptic equations; nonlinear boundary conditions;bifurcation
Subjects:Sciences > Mathematics
ID Code:44752
Deposited On:22 Sep 2017 11:16
Last Modified:12 Dec 2018 15:06

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