Existence Results for State-Dependent Maximal Monotone Differential Inclusions: Fixed Point Approach. (19th May 2022)

• Record Type: Journal Article
• Authors: Amiour, Fatima; Sene, Moustapha; Haddad, Tahar
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 7(2022)
• Page Start: 838
• Page End: 859
• Publication Date: 2022-05-19
• Subjects: Differential inclusion -- fixed point -- maximal monotone operators -- perturbations -- pseudo-distance; 34H05 -- 34K35 -- 28A25 -- 28C20 -- 35K90; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2059675
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, we give a new proof of the existence of absolutely continuous solutions for a class of first-order state-dependent maximal monotone differential inclusions. The existence result is obtained by using Schauder's fixed point theorem. In addition, a stability result is provided. Finally, using a suitable reduction of order technique, we give a new existence result for a general second-order state-dependent maximal monotone differential inclusion.