Periodic Boundary Value Problem For Several Kinds Of Differential Equations

Recently, periodic boundary value problems of the differential equations have become a very important area, and iterative technique and the method of the upper and lower solutions is a interesting while rather useful and important tool of which made use to prove the important inclusions in many papers and works, for details see([3-7, 19, 21]).This thesis of Master is composed of three chapters, which is mainly used the method and technique above to discuss the periodic boundary value problems for several kinds of differential equations.In chapter one, we study periodic boundary value problems relative to a general class of first-order functional differential equation: Through a comparison result, we obtained the existence conclusion of its solution and extremal solution.Chapter two mainly considers the periodic boundary value problem for nonlinear second-order functional differential equations: By the same way we got the sufficient condition of existence results on solutions for this class of problem.In the third chapter, we investigate the periodic boundary value problem for the mixed advanced differential equation: Applying the limitation to f, g, sufficient conditions when the problem has extremal solutions or a unique solution are given. Examples illustrate obtained results.