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  • Research Article
  • Open Access

Generalizations of the Lax-Milgram Theorem

Boundary Value Problems20072007:087104

https://doi.org/10.1155/2007/87104

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

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.

Keywords

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

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Authors’ 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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