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  • Research Article
  • Open Access

Generalizations of the Lax-Milgram Theorem

Boundary Value Problems20072007:087104

  • Received: 12 December 2006
  • Accepted: 19 April 2007
  • Published:


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.


  • Differential Equation
  • Banach Space
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation


Authors’ Affiliations

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