Existence Results for Integro-Differential Equations with Reflection

• DOI: 10.1080/01630563.2021.1933524
• Publication Date: 2021-06-12T14:55:06Z
• Authors: Mohsen Miraoui; Dušan D. Repovš
• Keywords: info:eu-repo/classification/udc/517.968.7; positive measure; pseudo almost automorphic solution; Mathematics - Analysis of PDEs; integro-differential equation; differential equation with reflection; FOS: Mathematics; 0101 mathematics; 34K30, 35B15; 01 natural sciences; Analysis of PDEs (math.AP)

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.