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