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中文摘要：
本文运用不动点指数理论讨论四阶三点边值问题u（4）（t）=g（t）f（u（t））,t∈（0,1）,u（0）=u＇（0）=u＂（β）=u＂（1）=0存在正解的充分条件，其中β∈[2/3,1）为常数，g∈C（[0,1],[0,∞））且g（t）不恒为零，t∈C（[0,∞）,[0,∞））.
英文摘要：
The authors consider a fourth order three-point boundary value problemu（4）（t）=g（t）f（u（t））,t∈（0,1）,u（0）=u＇（0）=u＂（β）=u＂（1）=0 where β∈[2/3,1） is constant, g∈C（[0,1],[0,∞））and g（t） is not identically zero on t∈C（[0,∞）,[0,∞））. The sufficient conditions of the existence of positive solutions is obtained by means of fixed point index theorem.
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