Journal of Applied Mathematics
Volume 2003 (2003), Issue 5, Pages 227-241
doi:10.1155/S1110757X03208032
A note on the variational structure of an elliptic system
involving critical Sobolev exponent
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.
Abstract
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.