Boundary Value Problems
Volume 2010 (2010), Article ID 175409, 15 pages
Research Article

Existence Result for a Class of Nonlinear Elliptic Systems on Punctured Unbounded Domains

Mathematics and Computer Science, Laurentian University, Sudbury, ON, P3E 2C6, Canada

Received 30 April 2009; Revised 10 November 2009; Accepted 13 January 2010

Academic Editor: Zhitao Zhang

Copyright © 2010 Fabrice Colin. 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.


We establish the existence of a nontrivial solution for systems with an arbitrary number of coupled Poisson equations with critical growth in punctured unbounded domains. The proof depends on a generalized linking theorem due to Krysewski and Szulkin, and on a concentration-compactness argument, proved by Frigon and the author. Applications to reaction-diffusion systems with skew gradient structure are also discussed in the last section.