Asymptotic Behavior Of Solutions Of Delay Differential Equations

Asymptotic Behavior of Solutions of Delay Differential EquationsThis dissertation mainly studies the asymptotic behavior of solutions of the following delay differential equationsandA series of new findings are acquired in it. And some of them improve or extend the related results in the literatures.Chapter 1 mainly introduces the background of the problem-researching and the recent development of the research in this field.Chapter 2 focuses on the asymptotic property of Eq.(O.l) with the oscillatory coefficients, It develops the related results in the recent Paper [3], and obtains the new sufficient conditions ensuring every solution of Eq.(O.l) to converge to zero.Chapter 3 concerns the asymptotic behavior of the neutral type delay differential equation (0,2) with positive and negative coefficients. It estabilishes some better results than the main results of Paper [9], and relaxes the general restriction of the coefficients Q1(t), Q2(t) > 0 and in Papers [10-12] as well.Chapter 4 presents some results of the asymptotic behavior for the general nonlinear delay differential equation (0.3). Eq.(0.3) contains many types of delay differential equations (see Papers [13, 23]). In this chapter, it not only relaxesthe strict restrictions of the coefficients in Paper [13], but also extends the applied scope of the main theorem in Paper [8], and improves the conditions for in Paper [23].Chapter 5 contains the asymptotic results for nonlinear delay differential equation (0.4). By extending the main results in Paper [4]. It obtains some new results. As an application for the following equationy'(t) + p(t)[a - y(t))}[b + y(t)]y(t - r) = 0, t>0,it gets a new result, which is different from that in Paper [17](see Corollary 5.1).In the last chapter, it discusses the asymptotic property of delay Logistic equation (0.5) with negative instantaneous terms and several delays, the results improve the corresponding results on the condition of 0 < c < 1 in Paper [30].