PERIODIC SOLUTION OF A SECOND ORDER OF DIFFERENTIAL EQUATIONS WITH HIGHER DERIVATIVES

The study deals with the existence, uniqueness, and stability of periodic solution of a second order of differential equations with higher derivatives. We provide a wide range of qualifications including the numerical-analytic method has been used by the Samoilenko method to investigate the existence and approximation of periodic solutions of nonlinear systems of the differential equations. We give an appropriate solutions of the problem, and extend the results of Shlapak to more general cases by assuming the weaker conditions for the functions