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Abstract and Applied Analysis
Volume 2017 (2017), Article ID 7236103, 13 pages
Research Article

A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem

Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

Correspondence should be addressed to Teffera M. Asfaw

Received 19 April 2017; Accepted 20 July 2017; Published 12 September 2017

Academic Editor: Stanislaw Migorski

Copyright © 2017 Teffera M. Asfaw. 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.


Let be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space . Let be maximal monotone, be bounded and of type and be compact with such that lies in (i.e., there exist and such that for all ). A new topological degree theory is developed for operators of the type . The theory is essential because no degree theory and/or existence result is available to address solvability of operator inclusions involving operators of the type , where is not defined everywhere. Consequently, new existence theorems are provided. The existence theorem due to Asfaw and Kartsatos is improved. The theory is applied to prove existence of weak solution (s) for a nonlinear parabolic problem in appropriate Sobolev spaces.