Positive Solutions Of Boundary Value Problems For Nonlinear Ordinary Differential Equations

Recently, boundary value problems of differential equations is an important branch of Modern Mathematics. On one hand, it associates with practical issues closely. On the other hand, the method of it has been driven by nonlinear functional analysis. In this way, the research of these issues is highly valued, and new theoretical achievements are constantly appearing, which lead a further development of boundary value problems of differential equations.The paper is divided into three chapters according to the contents.Chapter 1 is the introduction of this paper, which introduces the main contents of this paper.In chapter 2 the author considers the existence of at least three positive solutions for m-point boundary value problems of second order On condition that ai>Q(i=1,2,…m-2),0<ξ1<ξ2<…<ξm-2<1.The existence of at least three positive solutions is obtained by making use of the Leggett-Williams fixed point theorem in this paper, while f satisfied certain growth conditions. The conclusions extend and improve the main result of Ma Ruyun.In chapter 3 the author considers the nonlocal value problem for a nonlinear fourth order ordinary differential equation of the form where p, q:(0,1)â†'[0,+∞) are Lebesgue integrals,h:(0,1)â†'[0,∞) is continuous and allowed to be singular att= 0 and t=1. f:[0,∞)â†'[0,∞) is continuous.We show the existence of positive solutions of the above problem by applying the extended fixed point theorem concerning cone compression and expansion. The conclusions extend and improve the main result of Zhang Guowei.