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

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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
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2017
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Cambridge University Press
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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.
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Matemáticas (Matemáticas)
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12 Matemáticas
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https://hdl.handle.net/20.500.14352/18101
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