Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays

Open Access

Original research article

Author(s):

Hocine Gabsi^a, Abdelouaheb Ardjouni^b, Ahcene Djoudi^c

^a Department of Mathematics, University of El-Oued, El-Oued, Algeria
^b Department of Mathematics and Informatics, University of Souk Ahras, Souk Ahras, Algeria
^c Department of Mathematics, University of Annaba, Annaba, Algeria

Advances in the Theory of Nonlinear Analysis and its Applications 2(4), 184-194.

Received: March 3, 2018

Accepted: October 3, 2018

Published: October 10, 2018

Abstract

We consider two types of second-order neutral functional differential equations with infinite distributed delays and offer existence criteria for periodic solutions. During the process, we invert the integro-differential equations into equivalent integral equations and derive suitable fixed point mappings. We show that these mappings fit into the framework of Schauder’s fixed point theorem so that periodic solutions are readily obtained.

Keywords: Nonlinear neutral differential equations, periodic solutions, fixed point theorem, distributed delays.

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APA Style

Gabsi, H., Ardjouni, A., & Djoudi, A. (2018). Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays. Advances in the Theory of Nonlinear Analysis and its Application, 2(4), 184-194.