Bifurcation from infinity for reaction–diffusion equations under nonlinear boundary conditions
Published online by Cambridge University Press: 20 March 2017
Extract
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.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 3 , June 2017 , pp. 649 - 671
- Copyright
- Copyright © Royal Society of Edinburgh 2017
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