Periodic solutions of measure functional differential equations

• Autor(a) principal: Afonso, S. M. [UNESP]
• Data de Publicação: 2022
• Outros Autores: Bonotto, E. M., da Silva, Márcia R.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1016/j.jde.2021.11.031; http://hdl.handle.net/11449/222949
• topic: Impulsive differential equations; Measure functional differential equations; Periodic solutions; Topological transversality

In this article, we study the existence of periodic solutions for measure functional differential equations of the form x(t)=x(0)+∫0tf(s,xs)ds+∫0tg(s,xs)du(s), defined for every t∈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.