Journal of Applied Mathematics
Volume 2003 (2003), Issue 5, Pages 227-241

A note on the variational structure of an elliptic system involving critical Sobolev exponent

Mario Zuluaga

Departamento de Matemáticas, Universidad Nacional de Colombia, Bogota, Colombia

Received 22 August 2002; Revised 10 January 2003

Copyright © 2003 Mario Zuluaga. 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 consider an elliptic system involving critical growth conditions. We develop a technique of variational methods for elliptic systems. Using the well-known results of maximum principle for systems developed by Fleckinger et al. (1995), we can find positive solutions. Also, we generalize the systems results obtained (for the scalar case) by Brézis and Nirenberg (1983). Also, we give applications to biharmonic equations.