一类二阶三点边值问题多重正解的存在性

常微分方程的边值问题是微分方程的一个重要研究领域．线性常微分方程的多点边值问题的研究起源于Il＇in和Moiseev，其后Gupta研究了非线性三点边值问题．此后，许多作者借助于不动点理论，迭合度理论，Leray-Schauder非线性抉择及Krasnoselskii不动点定理等研究了更一般的非线性多点边值问题．研究了一类二阶非线性常微分方程的三点边值问题多重正解的存在性问题，在非线性项不满足超线性或次线性的条件下，利用不动点指数定理得到了至少存在两个正解的几个充分条件．所得结果是新的并且给出了几个例题以说明所得结果的应用．

Existence of multiple positive solutions for one kind of second-order three-point boundary value problem

The boundary value problem of ordinary differential equations is an important domain in differential equations.The study of multi-point boundary-value problems was initiated by Il'in and Moiseev.Then Gupta studied three-point boundary-value problems for nonlinear ordinary differential equations.Since then,by applying the Leray-Schauder continuation theorem,nonlinear alternative of Leary-Schauder,coincidence degree theory,and Krasnoselskii's fixed point theorem,many researchers have studied more general nonlinear multipoint bounadry value problem.In this paper,by using a fixed point index theorem,the existence of multiple positive solutions for one kind of second-order three-point boundary value problem is investigated.Several sufficient conditions for the existence of at least one or two positive solutions on the condition that nonlinear item is not satisfied with the super linear or sub-lineav are obtained.The results obtained are new and some examples are given to explain the main results.