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Generalizations of the Lax-Milgram Theorem

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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Correspondence to Dimosthenis Drivaliaris.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Drivaliaris, D., Yannakakis, N. Generalizations of the Lax-Milgram Theorem. Bound Value Probl 2007, 087104 (2007). https://doi.org/10.1155/2007/87104

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Keywords

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