Existence Of Solutions Of Boundary Value Problems For Higher-Order Nonlinear Differential Equations

In this paper, first, the author uses the upper-lower solution method and Schauder's fixed point theorem to show the existence of solutions of boundary value problem x'''(t)=f(t,x,x',x''), x(a)=A,x'(a)=B,x'(b)=C and we establish various results. At the same time, some examples are also given to illustrate some of the main results we obtain. Some results are generalized in this thesis, a result of the existence of solutions of boundary value problem is obtained.Then, Using the upper-lower solution method and some properties of the Green function,the author gives the existence theorems for fourth-order nonlinear boundary value problem Furthermore, based on the upper-lower solution method, we obtain the existence of solutions of nonlinear fourth-order differential equation with nonlinear three-point boundary conditions by modified function and developed the Nagumo condition.