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

Teffera M. Asfaw

Abstract and Applied Analysis, 2017, vol. 2017, issue 1

Abstract: 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‖ ≤ τ‖x‖ + 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.

Date: 2017
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2017/7236103

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2017:y:2017:i:1:n:7236103

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().