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Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities

Figueiredo, Giovany M. ; Ikoma, Norihisa ; Santos Júnior, João R.

Archive for rational mechanics and analysis, 2014-09, Vol.213 (3), p.931-979 [Periódico revisado por pares]

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Título:
Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities
Autor: Figueiredo, Giovany M. ; Ikoma, Norihisa ; Santos Júnior, João R.
Assuntos: Archives ; Classical Mechanics ; Complex Systems ; Concentrates ; Construction ; Fluid- and Aerodynamics ; Mathematical analysis ; Mathematical and Computational Physics ; Nonlinearity ; Physics ; Physics and Astronomy ; Texts ; Theoretical
É parte de: Archive for rational mechanics and analysis, 2014-09, Vol.213 (3), p.931-979
Notas: ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
Descrição: In this paper we study the existence and concentration behaviors of positive solutions to the Kirchhoff type equations - ε 2 M ε 2 - N ∫ R N | ∇ u | 2 d x Δ u + V ( x ) u = f ( u ) in R N , u ∈ H 1 ( R N ) , N ≧ 1 , where M and V are continuous functions. Under suitable conditions on M and general conditions on f , we construct a family of positive solutions ( u ε ) ε ∈ ( 0 , ε ~ ] which concentrates at a local minimum of V after extracting a subsequence ( ε k ).
Editor: Berlin/Heidelberg: Springer Berlin Heidelberg
Idioma: Inglês

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