中文摘要：

考虑一类三阶三点边值问题u″（t）＋a（t）f（u（t））=0,t∈（0,1）,u（0）=u′（1）-au′（η）=λ,其中,0〈η〈1,0〈α〈1/η,λ〉0,f满足超线性或者次线性条件,利用锥上的不动点定理,得到上述边值问题解的存在性结果.结果表明：文中方法进一步改进和推广了吴红萍的结果.

英文摘要：

We study the existence of positive solution to the following third-order three-point boundary value problems u″（t）＋a（t）f（u（t））=0,t∈（0,1）,u（0）=u′（1）-au′（η）=λ,where 0〈η〈1,0〈α〈1/η,λ〉0. By using fixed point theorem in cones,we obtain the existence of the positive solution if / is either superlinear or sublinear. Our results extend and improve some results made by Wu Hongping.