A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem
Author
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-09-12
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
Let X be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space X⁎.
Let T:X⊇D(T)→2X⁎ be maximal monotone, S:X→2X⁎ 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 σ≥0 and τ≥0 such that Cx≤τx+σ for all x∈D(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.
American Psychological Association (APA)
Asfaw, Teffera M.. 2017. A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem. Abstract and Applied Analysis،Vol. 2017, no. 2017, pp.1-13.
https://search.emarefa.net/detail/BIM-1120845
Modern Language Association (MLA)
Asfaw, Teffera M.. A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem. Abstract and Applied Analysis No. 2017 (2017), pp.1-13.
https://search.emarefa.net/detail/BIM-1120845
American Medical Association (AMA)
Asfaw, Teffera M.. A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem. Abstract and Applied Analysis. 2017. Vol. 2017, no. 2017, pp.1-13.
https://search.emarefa.net/detail/BIM-1120845
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1120845