Existence Results for Integro-Differential Equations with Reflection. (11th June 2021)

• Record Type: Journal Article
• Authors: Miraoui, Mohsen; Repovš, Dušan D.
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 8(2021)
• Page Start: 919
• Page End: 934
• Publication Date: 2021-06-11
• Subjects: Differential equation with reflection -- integro-differential equation -- positive measure -- pseudo almost automorphic solution; 34K30 -- 35B15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1933524
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We prove several important results concerning existence and uniqueness of pseudo almost automorphic (paa) solutions with measure for integro-differential equations with reflection. We use the properties of almost automorphic functions with measure and the Banach fixed point theorem, and we discuss two linear and nonlinear cases. We conclude with an example and some observations.