Solutions For Boundary Value Problems Of Nonlinear Differential Equations

With the rapid development of modern mathematics, nonlinear problem has become a important problem in the field of scientif-ic research, nonlinear functional analysis stems from the modern physics, medicine, biology, and other areas of the research. Non-linear functional analysis has initially formed system by scientific research personnel agent for a long time, and the theoretical results is gradually applied to every field, and it is an important tool of solving the phase for nonlinear problem. Among them, the integral boundary value problem is a hot spot of discussion in recent years, and it is the important domain in the research of differential equa-tions at present. In this paper, we study the solutions of several kinds of integral boundary value problem by using the fixed point theorem in cone, monotone iterative method and the cone Image theory,The thesis is divided into four sections according to contents.Chapter1Preference, we introduce the main contents of this paper.Chapter2In this chapter we discuss the nonlinear fractional differential equations boundary value problems: where n where k(t, s) By using the fixed point theorem in the cone and monotone iterative sequence, we obtained the existence and uniqueness of the solution of a class of nonlinear fractional order integro differential equations under the certain condition, and the error estimates are given.Chapter3This paper, We discuss the existence of positive so-lutions of the integration of high order nonlinear boundary value problem of fractional differential equations: where is Caputo fractional derivative. In this chapter, we obtained the existence of positive solutions of the boundary value problem (3.1.1) by using the fixed-point theorem and the properties of Green function and Guo-Krasnoselskii fixed point theoremChapter4In this chapter, and discussed the nonlinear frac-tional order calculus equation boundary value problem: where is Caputo fractional derivative. By the fixed-point theorem and Green function, we obtained the unique solution of a class of nonlinear fractional differential equation in certain conditions. By using the contraction mapping principle, we proved the existence of the positive solution under the certain conditions.