Existence results for gradient elliptic systems with nonlinear boundary conditions

We prove the existence of nontrivial solutions to the system Δpu = |u|p-2u, Δqv = |v| q-2v, on a bounded set of ℝN, with nonlinear coupling at the boundary given by |∇u|p-2∂u/∂ν = F u(x, u, v), |∇u|q-2∂v/∂ν = F v(x, u, v). The proofs are done under suitable assumptions on the potential F, and based...

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Detalles Bibliográficos
Autores: Fernandez Bonder, Julian, Martinez, Sandra Rita, Rossi, Julio Daniel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2007
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/125496
Acceso en línea:http://hdl.handle.net/11336/125496
Access Level:acceso abierto
Palabra clave:ELLIPTIC SYSTEMS
NONLINEAR BOUNDARY CONDITIONS
VARIATIONAL PROBLEMS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:We prove the existence of nontrivial solutions to the system Δpu = |u|p-2u, Δqv = |v| q-2v, on a bounded set of ℝN, with nonlinear coupling at the boundary given by |∇u|p-2∂u/∂ν = F u(x, u, v), |∇u|q-2∂v/∂ν = F v(x, u, v). The proofs are done under suitable assumptions on the potential F, and based on variational arguments. Our results include subcritical, resonant and critical growth on F.