Existence of a periodic solutions for certain system of nonlinear integro-differential equations

Abstract

In this paper we investigate the existence and approximation of the periodic solutions for certain systems of nonlinear integro-differential equations, by using the method of successive periodic approximation of ordinary differential equations which is given by A. M. Samoilenko. Also these investigation lead us to the improving the extending the above method.

The existence and approximation of the periodic solutions for system of first order nonlinear differential equationsby using Lebesgue integrable

“…The system of nonlinear differential equations (1) where the righthand side is defined, continuous and periodic in t and has period T in the domain (2) is said to be system -T if 1-The two sets are not empty…”

“…Samoilenko [7] assumed a numerical analytic method to study the periodic solutions for the ordinary differential equations and this method include uniformly sequences of the periodic functions as in the studies [1,2,3,5,6].…”

The existence and approximation of the periodic solutions for system of second order nonlinear differential equationsby using Lebesgue integrable

“…The system of nonlinear differential equations (1) where the righthand side defined and continuous and periodic in t of period T in the domain ( 2) is said to be system -T if 1-The two sets…”

“…There are many subjects in physics and technology use mathematical methods that depends on the nonlinear differential equations, and it became clear that the existence of the periodic solutions and its algorithm structure from more important problems in the present time, because of the great possibility for employment the electronic computers the numerical analytic method [6] which suggested by Samoilenko to study the periodic solutions for the linear and nonlinear differential equations became the effective mean to find the periodic solutions and its algorithm structure and this method include uniformly sequences of the periodic functions and the result of that study is the using of the periodic solutions on a wide rang in the difference of the new processes in industry and technology as in the studies [1,2,4,5]. We study in this paper the system of the non linear differential equations with the form ) 1 ........(…”

Existence, Uniqueness and Stability Solutions for New Nonlinear System of Integro-Differential Equations of Volterra Type

“…1996;Bailey, P.B., Shampine, L.F. and Waltman, P.E. 1968) and the Picard iteration can be used to generate the Taylor series solution for an ordinary differential equation (Butris, R. N. 1994;Butris R.N., 2015;Butris, R. N. and Ghada, Sh. J.…”