Existence And Uniqueness Of Periodic Solutions For Some Classes Of Functional Differential Equations With Multiple Deviating Arguments

In this thesis, we describe some important properties of the dynamic behaviors of several classes of functional differential equations , which includes the existence and uniqeuness of the periodic solutions. It is consists of four chapters. As the introductions, in Chapter 1, the background and history of several classes of first and second order functional differential equations are briefly addressed, and some preliminary results and definitions are given in this chapter. In Chapter 2, by using the continuation theorem of coincidence degree theory, we will give some new sufficient conditions for the existence and uniqeuness of the periodic solutions to a class of first order functional differential equation with two deviating arguments . The results of this chapter are new and they complement previously known results. In particular, they can also be used to the first order functional differential equation with multiple deviating arguments. In Chapter 3, we will give some new sufficient conditions the existence and uniqeuness of the periodic solutions to a class of Duffing equation with two deviating arguments. The results of this chapter are new and they complement previously known results. Moreover, they can also be used to the Duffing equation with multiple deviating arguments. In Chapter 4, Rayleigh equation with two deviating arguments are considered. Sufficient conditions for the existence of the periodic solutions are established by using the continuation theorem of coincidence degree theory . The results avoid the trantional conditions in the literature. and substantially extend and improve some important known results .