Qualitative Analysis Of Several Kinds Of Impulsive Differential Equations

This master thesis is composed of five chapters.which mainly studies the qualitative analysis of several kinds of impulsive differential equations.In chapter one. we briefly introduce the historical background and main tasks of this article.In chapter two, the asymptotic behavior of the solutions of a class of neutral type impulsive differential equation has been studied. Sufficient conditions for the asymptotic behavior of solutions of the system are obtained.Chapter three mainly considers the stability and asymptotic behavior of so-lutions of the second-order impulsive ordinary differential equations.In the process of the research, we try to weaken the condition of the known stability results in existing literature.and reflect the influence of pulse to stability.Chapter four is devoted to the studies of the oscillation of two class of impul-sive differential equations. This section firstly discusses the oscillation of a class of the second-order impulsive ordinary differential system. Our result improves and extends the results of the literature.Finally, we study the oscillation of a class of a first-order neutral differential equation of euler form with forced term. New sufficient conditions for the oscil-lation of all solutions of the equation are obtained. An example is also given to show the application of our results.