Qualitative Research On Solutions Of Several Classes Of Delay Differential Equations

This paper studies the asymptotic stability , asymptotic behavior of oscillatory solutions and periodic solutions of delay differential equationsA series of new results are obtained. And some of them improve or extend the related results in the literatures.Chapter 1 introduces the background of the problem-researching and the recent development of the research in this field.Chapter 2 focuses on the asymptotic stability of nonautonomous neutral differential equation (0.1). It obtains sufficient conditions for the zero solution of Eq.(0.1) to be uniformly stable as well as asymptotic stability, and improve or extends the part of results in the Paper [5,7].Chapter 3 concerns the 3/2- asymptotic stability of nonautonomous neutral differential equation with delays (0.2). Eq.(0.2) contains many types of delay differential equations (see Papers[5,7,21,76]).Our results improve or extend the related results in the literatures.Chapter 4 presents the asymptotic behavior of oscillatory solutions of forced nonautonomous neutral differential equation with delays(0.3). By extending the main results in Paper [16,23],we obtain some new results.Chapter 5 discusses the periodic solutions for a kind of Rayleigh equation with delay(0.4) . By employing the continuation theorem of coincidence degree theory, it obtains some new results on the existence of periodic solutions and...