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

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 infi...

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Detalles Bibliográficos
Autores: Mavinga, Nsoki, Pardo San Gil, Rosa María
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/18101
Acceso en línea:https://hdl.handle.net/20.500.14352/18101
Access Level:acceso abierto
Palabra clave:51
Steklov eigenvalues
elliptic equations
nonlinear boundary conditions
bifurcation
Matemáticas (Matemáticas)
12 Matemáticas
Descripción
Sumario: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.