Boundary Value Problems
Volume 2007 (2007), Article ID 87104, 9 pages
Research Article

Generalizations of the Lax-Milgram Theorem

Dimosthenis Drivaliaris1 and Nikos Yannakakis2

1Department of Financial and Management Engineering, University of the Aegean, 31 Fostini Street, Chios 82100, Greece
2Department of Mathematics, School of Applied Mathematics and Natural Sciences, National Technical University of Athens, Iroon Polytexneiou 9, Zografou 15780, Greece

Received 12 December 2006; Revised 8 March 2007; Accepted 19 April 2007

Academic Editor: Patrick J. Rabier

Copyright © 2007 Dimosthenis Drivaliaris and Nikos Yannakakis. 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 prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular, we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all bounded linear functionals of the latter. We also give two applications to singular differential equations.