On the existence of periodic solutions for various kinds of differantial equations

This thesis consists of seven chapters. In the first chapter, some works on the existence of periodic solutions of differantial equations can be found in the literature are summarized. In the second chapter, the material and method to be used in the thesis are stated. In the third chapter, the method used to examine the existence of periodic solutions of the differential equations discussed in the thesis, some basic definitions, lemmas and theorems are given. In the fourth chapter of the thesis, with the help of the second method of Lyapunov, the existence of periodic solutions of two nonlinear differential equations of second order with constant and variable delays, respectively, are investigated. In the fifth chapter, sufficient conditions for the existence of periodic solutions of two nonlinear differential equations of third order with multiple delays are obtained. In the sixth chapter of the thesis, by means of the Lyapunov's second method, sufficient conditions for the existence, stability and boundedness of the solutions of a nonlinear differential equation of fourth order with multiple time lags are obtained. In the last chapter, which is the final chapter of the thesis, a short conclusion related to the subject of the thesis is given.