Boundary Value Problems Existence Of Solutions In Several Categories

This thesis investigates the existence of solutions for some class of boundary value problems of nonlinear differential equations. The existence of positive solutions for two class of nonlinear differential equations boundary value problems are obtained by using the fixed point theorems; we investigate the existence of solution for a kind of boundary value problem of nonlinear integro-dfferential equation by applying the monotone iterative technique and the method of upper and lower solutions. The thesis consists of four chapters.Chapter 1 is preface. The historical background of the problems and the significance of this thesis are introduced. Boundary value problems occur in various fields of natural science. The existence of solutions for boundary value problems attracts much attention of many famous mathematicians all around the world. The recent developments on existence of solutions for boundary value problems of nonlinear differential equations are given. And some knowledge needed in this thesis are also summarized.In Chapter 2, using the Guo-Krasnosel'skii fixed point theorem and the Schauder fixed point theorems, we discuss the existence of monotone positive solutions of a class of m-point boundary value problems for the n-order nonlinear differential equations boundary value problems with nonhomogeneous boundary conditions. A result of the existence of monotone positive solutions is obtained.In Chapter 3, using the Schauder fixed point theorem, we investigate the existence of positive solutions of a class of three-point boundary value problems for the two order nonlinear impulsive differential equations boundary value problems with nonhomogeneous boundary conditions. A result of the existence of positive solutions is obtained.In Chapter 4, firstly, applying the impulsive differential inequality, a new comparison principle of a class of impulsive integro-differential equation boundary value problems with nonlinear boundary condition is obtained. Secondly, using the monotone iterative technique and the method of upper and lower solutions, this class of second-order impulsive integro-differential equation with nonlinear boundary condition, the existence of extreme solutions is discussed.