Existence And Uniqueness Of The Boundary Value Problem To Several Classes Of Differential Equations

In this paper, by using cone theory, lower-upper solution method in the reversed order, some fixed point theorems, we discuss the existence and uniqueness of solution to several classes of differential equations. Some new results are obtained, and some relevant results are extended and improved. The structure of this paper as follows.In the first chapter, we introduce the background of the discussed problem of this thesis briefly, and we state the main results of this thesis concretely. In the second chapter, by using lower-upper solution method in the reversed order, we investigate second-order three-point boundary value problem as follows: Where f∈C(I×R×R,R),I=[0,1],the sufficient conditions for the existence and uniqueness of solution by using monotone iterative method are obtained.In the third chapter, by using a new fixed point theorem of u0-concave operator, we study the second-order three-point boundary value problem of impulsive differential equation: Where f∈C(J×R×R,R),Ik,Jk∈C(R,R),0=t0