Characterization of the Solvability of Generalized Constrained Variational Equations
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Hindawi Publishing Corporation
Inf-sup conditionsImpulsive differential equationsFinite elementSpacesTheoremMultiplicity
Ruiz Galán, M. Characterization of the Solvability of Generalized Constrained Variational Equations. Abstract and Applied Analysis, 2012: 247425 (2012). [http://hdl.handle.net/10481/31363]
PatrocinadorThis research is partially supported by the Junta de Andaluca Grant FQM359.
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.