Existence Of Solutions For Differential Equations

In this paper,we study the existence of solutions of three-point boundary value problems for third order differential equations and integral boundary value problems of second-order integral differential equations in Banach spaces by using the fixed point theorem.In the first chapter,The definition of related theorem in this paper is introduced briefly.In the second chapter,some basic definitions of ordinary differential equations in Banach space are introduced.In the third chapter,we study the existence of solutions of nonlinear third-order three-point boundary value problems in Banach spaces by using the Sadvoskii fixed point theorem,constructing monotone iterative processes of quasi-upper and lower solutions and compact computation of non-compact measures.In the fourth chapter,we prove a fixed point theorem of mixed monotone operators and study the existence and uniqueness of so-lutions of second order integro-differential equations with integral boundary value problems.