On the existence and concentration of positive solutions to a class of quasilinear elliptic problems on R

Autor(es)

Alves, Claudianor O. ^[1] ; Miyagaki, Olimpio H. ^[2] ; Monari Soares, Sergio H. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Fed Campina Grande, Unidade Acad Matemat & Estat, BR-58109970 Campina Grande, PB - Brazil

^[2] Univ Fed Juiz de Fora, Dept Matemat, BR-36036330 Juiz De Fora, MG - Brazil

^[3] Univ Sao Paulo, ICMC USP, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Mathematische Nachrichten; v. 284, n. 14-15, p. 1784-1795, OCT 2011.
• Citações Web of Science: 9

Resumo

This paper is concerned with the existence and concentration of positive solutions for the following quasilinear equation epsilon(2)v `' - V(x)v + |v|(q-1)v + epsilon(2)k(|v|(2))'' v = 0, x is an element of R. The proof relies on variational methods by using directly the functional associated with the problem in an appropriate Sobolev space. It was found a family of solutions [u(epsilon)] concentrating around a local minimum of V as epsilon tends to zero. (C) 2011 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim (AU)

• Processo FAPESP: 07/03399-0 - Claudianor Oliveira Alves | Centro de Ciências e Tecnologia/UFCG - Brasil
• Beneficiário: Sergio Henrique Monari Soares
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil