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

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

• Second order,Nonlinear neutral differential equations,Periodic solutions,Fixed point theorem,Distributed delays.

References

1. 1) A. Ardjouni, A. Rezaiguia and A. Djoudi, Existence of positive periodic solutions for two types of second-order nonlinear neutral differential equations with infinite distributed delay, J. Appl. Math. Comput. (2015) 47:291--314.
2. A. Ardjouni, A. Djoudi, Existence of positive periodic solutions for two types of second order nonlinear neutral differential equations with variable delay, Proyecciones J. Math. 32 (4) (2013) 377--391.
3. A. Ardjouni, A. Djoudi, Existence of periodic solutions in totally nonlinear neutral dynamic equations with variable delay on a time scale, Math. Eng. Sci. Aerosp. MESA 4 (3) (2013) 305--318.
4. A. Ardjouni, A. Djoudi, Existence of positive periodic solutions for two kinds of nonlinear neutral differential equations with variable delay, Dyn. Continuous Discrete Impulsive Syst. Ser. A Math. Anal. 20 (2013) 357--366.