Characterization of the Solvability of Generalized Constrained Variational Equations
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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/247425 |
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| _version_ | 1850167881792225280 |
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| author | Manuel Ruiz Galán |
| author_facet | Manuel Ruiz Galán |
| author_sort | Manuel Ruiz Galán |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-df33c54434ec4289a256e04eb19ff5d2 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-df33c54434ec4289a256e04eb19ff5d22025-08-20T02:21:06ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/247425247425Characterization of the Solvability of Generalized Constrained Variational EquationsManuel Ruiz Galán0Departamento de Matemática Aplicada, E.T.S. de Ingeniería de Edificación, Universidad de Granada, c/Severo Ochoa s/n, 18071 Granada, SpainIn 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.http://dx.doi.org/10.1155/2012/247425 |
| spellingShingle | Manuel Ruiz Galán Characterization of the Solvability of Generalized Constrained Variational Equations Abstract and Applied Analysis |
| title | Characterization of the Solvability of Generalized Constrained Variational Equations |
| title_full | Characterization of the Solvability of Generalized Constrained Variational Equations |
| title_fullStr | Characterization of the Solvability of Generalized Constrained Variational Equations |
| title_full_unstemmed | Characterization of the Solvability of Generalized Constrained Variational Equations |
| title_short | Characterization of the Solvability of Generalized Constrained Variational Equations |
| title_sort | characterization of the solvability of generalized constrained variational equations |
| url | http://dx.doi.org/10.1155/2012/247425 |
| work_keys_str_mv | AT manuelruizgalan characterizationofthesolvabilityofgeneralizedconstrainedvariationalequations |