Class Of Differential Equations Are Solutions

Along with the development of scientific technology,modern physics and applied mathmatics,many kind of non-linear problems have emerged.Those prob-lems have increasingly aroused people's widespread attentions,which greatly urge the non-linear functional analysis to be better improved.The semi-positone prob-lems and singular boundary value problems are the topic points.Many authors have studied in every asperts. In this paper using cone theorem,fixed theorem as well as fixed point theorem, we discuss several classes of differential equation boundary value problems and talk about their existences of postive solutions.In Chapter 1, we use the cone theory and cone expansion and compression theorem to study the existence of postive solutions for second-order three-point boundary value problem in Banach space whereηis subjected to (0,1)andλ>0 is parameter,h(t) is allowed to be singular at t=0,1.In Chapter 2, by talking about the parameter ofλ> 0, we use the cone expansion and compression theorem to study the postive solutions of forth-order semi-positone boundary value problem whereλ>0 is parameter and h(t) is allowed to be singular at t=0,1.In Chapter 3, we use the cone theory and fixed point theorem to investigate the postive solutions of three-order three-point boundary value problem where 0<η<1,1<α<1/ηand a(t)is singular at t=0,1.