The Periodic Solutions And Periodic Boundary Value Problems For Functional Differential Equations

In this thesis of master, we investigate the existence of periodic solutions and periodic boundary value problems for functional differential equations.The questions of existence of periodic solutions and periodic boundary value problems for differential equations is studied many authors,expecially the quustions of the second order functional differential equations. These results extend some of the existing literature.It is consists of two chapters.In chapter 1, we discuss the existence of periodic solutions for second-order differential equationwhere a_i∈R,(?)_i∈R,g,p∈C(R),p(t + T)=p(t).By the means of the Browner degree theory and Mawhin theory, we derive two important lemmas. By the lemmas,criteria on the existence of periodic solutions are obtained.We generalize some known results,and obtain some existence and nonexistence results.In chapter 2, we discuss periodic boundary value problems for second-order functional differential equationwhere f∈C((?)×R~2,R),0≤θ(t)≤t.We show that the method of monotone iterative technique is valid to obtain two monotone sequences that coverge uniformly to extremal solutions this second-order functional differential equation. The method of upper and lower solutions with reversed ordering is employed.By establishing comparison results, we obtain the existence of extremal solution about the functional differential equations.The result extends some of the existing literature.