The Study Of Existence Of Multiple Solutions Of Boundary Value Problems Of Ordinary Differential Equations

Boundary value problems of ordinary differential equations have diverse sources and applications in pratice and theory respectively. Especially, existence of positive solution(s) occupies an important place in this research, because of its prominent pratical significance. This thesis focuses on existence of positive solution(s) for some boundary value problems of several ordinary differential equations. There are four chapters. In first chapter, we mainly present research histories and situations of several research directions with respect to positive solution. In second chapter, by introducing a new functional, we generalize the existing cone expansion and compression fixed point theorems and apply it to a second order two point boundary value problem. In third chapter, we extend a mutiple-solution theorem to nth order two point boundary value problem with the nonlinear term depending on all lower order derivatives. In last chapter, we consider a second order two point boundary value problem with sign-changing Green's function, and obtain existence of positive solution for it.