Generalizations of the Lax-Milgram Theorem

  • Dimosthenis Drivaliaris1Email author and

    Affiliated with

    • Nikos Yannakakis2

      Affiliated with

      Boundary Value Problems20072007:087104

      DOI: 10.1155/2007/87104

      Received: 12 December 2006

      Accepted: 19 April 2007

      Published: 21 May 2007


      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.


      Authors’ Affiliations

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


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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.