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

Mario Zuluaga

 Departamento de Matemáticas, Universidad Nacional de Colombia, Bogota, Colombia
Received 22 August 2002; Revised 10 January 2003

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.