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Generalizations of the Lax-Milgram Theorem


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 (, 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).

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