The Problem Of Periodic Solutions For Second Order Duffing Equation With Deviating Argument

By applying Mawhin's continuation theoren of coincidence degree , we study the problems of periodic solutions for second order Duffing equations with deviating argument , and obtain some new results. Our work improves and extends the results of known dissertation. The whole thesis contains three chapters.In the first chapter, we concisely introduce the background of the subjects relevant to this dissertation. Then we introduce known progress on study of Duffing equation and the main work done in the thesis.In the second chapter, we introduce some important lemmas which are the foundation of the dissertation.In the third chapter, we devote to the problems of periodic solutions for two kinds of Duffing equations with deviating argument. In the first section, we study the following equation x"(t) +β(t)g(x(t - (?))) = p(t) , in which we only require that the sign ofβ(t) is unchanged and the growth condition imposed on function g(x) is one-sided linear. In the second section, the result of existence for periodic solution to another Duffing equation x"(t) + bx~n + g(x(t - (?))) = p(t) is given , where n is positive. The work improves and extends the corresponding results in the past.