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Abstract and Applied Analysis
Volume 2012, Article ID 247425, 36 pages
http://dx.doi.org/10.1155/2012/247425
Research Article

Characterization of the Solvability of Generalized Constrained Variational Equations

Departamento de Matemática Aplicada, E.T.S. de Ingeniería de Edificación, Universidad de Granada, c/Severo Ochoa s/n, 18071 Granada, Spain

Received 4 December 2011; Accepted 30 January 2012

Academic Editor: Juan J. Nieto

Copyright © 2012 Manuel Ruiz Galán. 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.

Abstract

In a general context, that of the locally convex spaces, we characterize the existence of a solution for certain variational equations with constraints. For the normed case and in the presence of some kind of compactness of the closed unit ball, more specifically, when we deal with reflexive spaces or, in a more general way, with dual spaces, we deduce results implying the existence of a unique weak solution for a wide class of linear elliptic boundary value problems that do not admit a classical treatment. Finally, we apply our statements to the study of linear impulsive differential equations, extending previously stated results.