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2017 A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem
Teffera M. Asfaw
Abstr. Appl. Anal. 2017: 1-13 (2017). DOI: 10.1155/2017/7236103

Abstract

Let X be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space X. Let T:XD(T)2X be maximal monotone, S:X2X be bounded and of type (S+), and C:D(C)X be compact with D(T)D(C) such that C lies in Γστ (i.e., there exist σ0 and τ0 such that Cxτx+σ for all xD(C)). A new topological degree theory is developed for operators of the type T+S+C. 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 T+S+C, where C 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.

Citation

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Teffera M. Asfaw. "A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem." Abstr. Appl. Anal. 2017 1 - 13, 2017. https://doi.org/10.1155/2017/7236103

Information

Received: 19 April 2017; Accepted: 20 July 2017; Published: 2017
First available in Project Euclid: 11 October 2017

zbMATH: 06929564
MathSciNet: MR3705452
Digital Object Identifier: 10.1155/2017/7236103

Rights: Copyright © 2017 Hindawi

Vol.2017 • 2017
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