Existence Of Solutions Of Boundary Value Problems To Nonlinear Differential Equations

This dissertation is concerned with boundary value problems of nonlinear differential equations, as well as BVPs of fractional differential equations which have quickly developed in the last few years.In the chapter one, the summary and development of boundary value problems for nonlinear differential and fractional differential equations are introduced. Main results of this dissertation are summarized.Chapter two is concerned with the third-point boundary value problems for nonlinear differential equations with P-Laplacion. By using Guo-Krasnoselskii fixed point theorem, the sufficient conditions under which ensure the existence of positive solutions are obtained.In the chapter three, the four-point boundary value problem of fractional differential equations is considered. By virtue of Krasnoselskii fixed point theorem and some analysis techniques, the existence of solutions is obtained. An example is given to illustrate the main results obtained there.Chapter four is concerned with non-homogeneous fractional delayed differential equations. By using Laplace transform, the existence and uniqueness of solutions are obtained.