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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

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/087104

Received:12 December 2006
Revisions received:8 March 2007
Accepted:19 April 2007
Published:21 May 2007

© 2007 Drivaliaris and 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.


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