Abstract and Applied Analysis
Volume 2012 (2012), Article ID 137379, 16 pages
http://dx.doi.org/10.1155/2012/137379
Research Article

Existence of Solutions of a Nonlocal Elliptic System via Galerkin Method

Alberto Cabada1 and Francisco Julio S. A. Corrêa2

1Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
2Unidade Acadêmica de Matemática e Estatística, Centro de Ciências e Tecnologia, Universidade Federal de Campina Grande, 58.109-979 Campina Grande, Brazil

Received 2 February 2012; Accepted 28 February 2012

Academic Editor: Pavel Drábek

Copyright © 2012 Alberto Cabada and Francisco Julio S. A. Corrêa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By means of the Galerkin method and by using a suitable version of the Brouwer fixed-point theorem, we establish the existence of at least one positive solution of a nonlocal elliptic N-dimensional system coupled with Dirichlet boundary conditions.