Existence Of Periodic Solutions And Boundedness Of Solutions For Two Classes Of Functional Differential Equations

In this thesis,based on the framework of generalized ordinary differential equations,first of all,it is based on the corresponding relation between impulsive retarded functional differential equations and generalized ordinary differential equations,with the help of the existence of periodic solutions of generalized ordinary differential equations and the continuation theorem in Mawhin’s coincidence degree theory,the sufficient conditions for the existence of periodic solutions of impulsive retarded functional differential equations are presented,the existence theorem of the periodic solution of impulsive retarded functional differential equations is established.Secondly,based on the equivalence between measure neutral functional differential equations and generalized ordinary differential equations,by virtue of the boundedness of solutions of generalized ordinary differential equations and and Lyapunov functional,sufficient conditions for uniformly bounded and uniformly ultimately bounded of solutions of measure neutral functional differential equations are presented,and the boundedness theorems of solutions of measure neutral functional differential equations are established.In addition,the boundedness of solutions of a class of impulsive neutral functional differential equations is proved by an example.