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Journal of Mathematics
Volume 2013, Article ID 301319, 6 pages
http://dx.doi.org/10.1155/2013/301319
Research Article

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

Department of Public Health, Western Kentucky University, 1906 College Heights Boulevard, Bowling Green, KY 42104, USA

Received 7 November 2012; Accepted 8 January 2013

Academic Editor: Jen-Chih Yao

Copyright © 2013 Boubakari Ibrahimou. 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

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.