Periodic solutions of second-order nonlinear system of integro-differential equations unsolvable for the highest derivative

ABSTRACT In this paper we study the existence and approximation of the periodic solutions for certain systems of second-order of integro-differential equations unsolvable for the highest derivative by using the numerical analytic method for ordinary differential equations of A. M. Samoilenko which given. Also these investigation lead us to the improving the extending the above method.