Asymptotic Properties Of Several Classes Of Nonlinear Differential Equations

In this thesis, we study some important asymptotic properties of several classes of nonlinear differential equations. It consists of four chapters.In chapter 1, the background and history of problems which we discuss in this thesis are briefly addressed. Besides, some definitions and basic results are given in this chapter.In chapter2, we discuss the following nonlinear Duffing equation with a deviating argument:We give some new sufficient conditions for the existence and uniqueness of almost periodic solutions of the above Duffing equation. In addition, in the case ofIn chapter 3, we investigate the following general dynamical systems :which unify some extensively studied shunting inhibitory cellular neural networks with delays. Under some suitable conditions, a new theorem is established to ensure that all the solutions of the dynamical systems converge exponentially to the zero point, which substantially extend and improve some important results in the literature.In chapter 4, we consider the following Liénard-type equation:Sufficient conditions for the existence and uniqueness of anti-periodic solutions of the equation are established .