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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Alves, Claudianor O. [1] ; Miyagaki, Olimpio H. [2] ; Monari Soares, Sergio H. [3]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: Mathematische Nachrichten; v. 284, n. 14-15, p. 1784-1795, OCT 2011.
Web of Science Citations: 9
Abstract

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)