Multiplicity of solutions for a biharmonic equation with subcritical or critical growth

We consider the fourth-order problem {ε4△2u + V(x)u = f(u) +γ |U|2..-2u inRN u ∈ H 2(RN), where ε > 0, N ≥ 5, V is a positive continuous potential, is a function with subcritical growth and γ ∈ {0,1}. We relate the number of solutions with the topology of the set where V attain its minimum values...

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Detalles Bibliográficos
Autores: Figueiredo, Giovany M., Pimenta, Marcos T. O. [UNESP]
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/227615
Acceso en línea:http://dx.doi.org/10.36045/bbms/1378314513
http://hdl.handle.net/11449/227615
Access Level:acceso abierto
Palabra clave:Biharmonic equations
Nontrivial solutions
Variational methods
Descripción
Sumario:We consider the fourth-order problem {ε4△2u + V(x)u = f(u) +γ |U|2..-2u inRN u ∈ H 2(RN), where ε > 0, N ≥ 5, V is a positive continuous potential, is a function with subcritical growth and γ ∈ {0,1}. We relate the number of solutions with the topology of the set where V attain its minimum values. We consider the subcritical case γ = 0 and the critical case γ = 1. In the proofs we apply Ljusternik-Schnirelmann theory.