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中文摘要：
该文讨论了偶数阶边值问题（-1）^my^（2m）=f（t,y）,0≤t≤1,αi＋1y^（2i）（0）-βi＋1y^（2i＋1）（0）=0,γi＋1y^（2i）（1）＋δi＋1y^（2i＋1）（1）=0,0≤i≤m-1正解的存在性．借助于Leggett-Williams不动点定理，建立了该问题存在三个及任意奇数个正解的充分条件．
英文摘要：
In this paper the authors discuss the existence of positive solution to the following even order boundary value problem （-1）^my^（2m）=f（t,y）,0≤t≤1,αi＋1y^（2i）（0）-βi＋1y^（2i＋1）（0）=0,γi＋1y^（2i）（1）＋δi＋1y^（2i＋1）（1）=0,0≤i≤m-1.Sufficient conditions are obtained for existence of three or arbitrary odd positive solutions of the above problem by using Leggett-Williams fixed point theorem.
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