Stability And Boundedness Of Impulsive Retarded Functional Differential Equations

In this dissertation,we mainly study the solutions of stability and boundedness of impulsive retarded functional differential equations.Firstly,by using the equivalent relation of impulsive retarded functional differential equations and generalized ordinary differential equations,the theorem of the existence and uniqueness of maximal solution of impulsive retarded functional differential equations is established.Furthermore,combining with Lyapunov functional,on the one hand,the theorems concerning stability of impulsive retarded functional differential equations are established.On the other hand,by discussing the relevant theorems concerning boundedness of impulsive retarded functional differential equations,the theorem of the converse Lyapunov theorems concerning uniform boundedness of impulsive retarded functional differential equations is established.Finally,by using the results of the above work,we obtain the relationship between uniform stability and uniform boundedness of impulsive retarded functional differential equations.