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Eigenvalue for Densely Defined Perturbations of Multivalued Maximal Monotone Operators in Reflexive Banach Spaces

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  • Boubakari Ibrahimou

Abstract

Let be a real reflexive Banach space and let be its dual. Let be open and bounded such that . Let be maximal monotone with and . Using the topological degree theory developed by Kartsatos and Quarcoo we study the eigenvalue problem where the operator is a single-valued of class . The existence of continuous branches of eigenvectors of infinite length then could be easily extended to the case where the operator is multivalued and is investigated.

Suggested Citation

  • Boubakari Ibrahimou, 2013. "Eigenvalue for Densely Defined Perturbations of Multivalued Maximal Monotone Operators in Reflexive Banach Spaces," Journal of Mathematics, Hindawi, vol. 2013, pages 1-6, February.
    • Handle: RePEc:hin:jjmath:301319
    DOI: 10.1155/2013/301319
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    References listed on IDEAS

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    1. Athanassios G. Kartsatos & Igor V. Skrypnik, 2005. "A new topological degree theory for densely defined quasibounded ( S ˜ + ) -perturbations of multivalued maximal monotone operators in reflexive Banach spaces," Abstract and Applied Analysis, Hindawi, vol. 2005, pages 1-38, January.
    2. Juha Berkovits, 1999. "On the degree theory for densely defined mappings of class ( S + ) L," Abstract and Applied Analysis, Hindawi, vol. 4, pages 1-12, January.
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