Stability Of Sets For Functional Differential Equations With Impulsive Effects

In this paper, we thoroughly investigate stability of sets for impulsive functional differential equations as follows:using Liapunov functions with Razumikhin techniques or Liapunov like functionals, criteria on stability of sets are established for the above system,our results generalize or improve the corresponding results in the references. This paper is divided into three chapters.In chapter one, we summarize notion, research background and some question on stability of sets with respect of the solutions for impulsive functional differential equations, and the main work of the paper is given.In chapter two, given basic knowledge, definitions and appropriate restrictive conditions in section one; criteria on uniform or uniform asymphoticstability of sets for the above impulsive functional differential systemare established using Liapunov functions with Razumikhin techniques in section two; In section three, some examples are also discussed to illustratethe results of section two.In chapter three, a function P in the Liapunov functions with Razumikhintechniques is searched very difficultly, so for the sake of avoidance, stability of sets results for the above impulsive functional equations are established by means of Liapunov like functionals techniques, which are generalized or improved combing stability of sets for differential equations and the stability of zero solution for impulsive (functional) differential equations.