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Characterization of the Solvability of Generalized Constrained Variational Equations

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  • Manuel Ruiz Galán

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.

Suggested Citation

  • Manuel Ruiz Galán, 2012. "Characterization of the Solvability of Generalized Constrained Variational Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:247425
    DOI: 10.1155/2012/247425
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    References listed on IDEAS

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    1. Hongxia Fan & Yongxiang Li, 2011. "Multiple Positive Solutions for Singular Periodic Boundary Value Problems of Impulsive Differential Equations in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-12, October.
    2. Hongxia Fan & Yongxiang Li, 2011. "Multiple Positive Solutions for Singular Periodic Boundary Value Problems of Impulsive Differential Equations in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
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