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中文摘要：
考虑一类带有参数的非线性三阶三点边值问题．通过定义指标io和i∞，从而根据它们的不同取值，对于参。数适当的变化范围，建立该边值问题正解的存在性以及不存在性准则．所用的工具为不动点指数理论．
英文摘要：
A class of nonlinear three-order three-point boundary value problems with parameters was considereal. By defining indices io and i∞ and assigning values to them, some criteria for determination of existence and non-existence of positive solutions to this boundary value problem were established for an appropriate range of parameters. The main tool used was the theory of the fixed-point index.
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