Boundary Value Problems 
Volume 2007 (2007), Article ID 87104, 9 pages
doi:10.1155/2007/87104
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

Recommended by Patrick J. Rabier

Abstract

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.