Periodic solutions of measure functional differential

Author(s)

Afonso, S. M. ^[1] ; Bonotto, E. M. ^[2] ; da Silva, Marcia R. ^[2]

Affiliation

^[1] Univ Estadual Paulista, Inst Geociencias & Ciencias Exatas, UNESP, Campus Rio Claro, Ave 24-A, 1515, BR-13506900 Sao Paulo - Brazil

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Campus Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Journal of Differential Equations; v. 309, p. 196-230, FEB 5 2022.
• Web of Science Citations: 0

Abstract

In this article, we study the existence of periodic solutions for measure functional differential equations of the form x(t) = x(0) + integral(t)(0) f (s, x(s))ds + integral(t)(0) g(s, x(s))du(s), defined for every t is an element of R, under suitable assumptions on f, g and u, where the integrals on the right-hand side exist in the Perron and Perron-Stieltjes sense, respectively. We make use of a topological transversality theorem to obtain the main result. Some examples are presented to illustrate the developed theory. Moreover, we apply the results obtained in the context of measure functional differential equations to establish the existence of periodic solutions for a class of impulsive functional differential equations. (C) 2021 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 19/03188-7 - Recursive properties and oscillation of impulsive dynamical systems
• Grantee: Everaldo de Mello Bonotto
• Support Opportunities: Regular Research Grants