Open Access

Generalizations of the Lax-Milgram Theorem

Boundary Value Problems20072007:087104

DOI: 10.1155/2007/87104

Received: 12 December 2006

Accepted: 19 April 2007

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.

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Authors’ Affiliations

(1)
Department of Financial and Management Engineering, University of the Aegean
(2)
Department of Mathematics, School of Applied Mathematics and Natural Sciences, National Technical University of Athens

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Copyright

© D. Drivaliaris and N. Yannakakis. 2007

This article is published under license to BioMed Central Ltd. 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.