Types Of Nonlinear Ordinary Differential Equations Of Non-existence Of Solution Of Local Problems

This thesis is devoted to existence of solutions or positive solutions of nonlinear and nonlocal problems of ordinary differential equations.It consists of seven chapters.In chapter one,the background and present situation are introduced and summarized for the study of nonlocal problem of ordinary differential equations.In chapter two,a kind of nonhomogeneous two-order three-point boundary value problem is studied,using Schauder fixed-point theorem and one fixed-point index theorem,sufficient conditions are obtained for existence of positive solutions for this boundary value problem.In chapter three,a kind of nonhomogeneous m-point boundary value problem with p-Laplacian is studied,under suitable conditions,using fixed point theorem,we obtain conclution that there exist positive solutions for this boundary value problem.In chapter four,we are devoted to a kind of nonhomogeneous m-point boundary value problem with p-Laplacian of singularity,under suitable conditions,using fixed point theorem,we obtain some conclutions of the existence of positive solutions for this boundary value problem.In chapter five,a kind of nonlinear m-point boundary Value problem with p-Laplacian with two sets of boundary value conditions is studied, using Leggett-Williams fixed point theorem,sufficient conditions for existence of triple positive solutions are established for anyone of the boundary value problems.In chapter six,a kind of m-point boundary value problem with p-Laplacian with two sets of boundary value conditions is studied,under suitable conditions,using Leray-Schauder continuation theorem,we show the existence of asolutions for anyone of the boundary value problems.In chapter seven,a kind of m-point boundary value problem with two sets of boundary value conditions is studied,using Leray-Schauder continuation theorem,sufficient conditions are established for existence of a solution for anyone of the boundary value problems.