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Open Access Research Article

Generalizations of the Lax-Milgram Theorem

Dimosthenis Drivaliaris1* and Nikos Yannakakis2

Author Affiliations

1 Department of Financial and Management Engineering, University of the Aegean, 31 Fostini Street, Chios 82100, Greece

2 Department of Mathematics, School of Applied Mathematics and Natural Sciences, National Technical University of Athens, Iroon Polytexneiou 9, Zografou 15780, Greece

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Boundary Value Problems 2007, 2007:087104  doi:10.1155/2007/87104

Published: 21 May 2007

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.