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中文摘要：
运用上下解方法及不动点指数理论，在非齐次边界条件下讨论了三阶三点边值问题u″′（t）＋a（t）f（t））=0,t∈（0,1）,u（0）=λ1,u′（0）=λ2,u′（1）-au′（η）=λ3正解的存在性和不存在性，并且给出了该问题至少存在一个正解，两个正解及无正解时参数（λ1，λ2，λ3）的最优取值范围。其中（λ1，λ2，λ3）∈R3＊／｜0,0,0）｜为参数，η∈（0,1）,α∈[0,1/η）为常数，α∈С（（0，1），[0，＋∞）），f∈С（[0,＋∞）,[0,＋∞））。
英文摘要：
By using the lower and upper solutions method and fixed point index theory, we study the existence and non- existence of positive solutions of nonhomogeneous boundary value problem u″′（t）＋a（t）f（t））=0,t∈（0,1）, u（0）=λ1,u′（0）=λ2,u′（1）-au′（η）=λ3 and given the optimal regions of （λ1,λ2,λ3） when the above problem at least exist one positive solution, two positive solutions and no positive solution, respectively. Where （λ1,λ2,λ3） ∈R3＊／｜0,0,0）｜ tare parameters, η∈（0,1）,α∈[0,1/η）are constants,α∈С（（0,1）,[0,＋∞））,f∈С（[0,＋∞）,[0,＋∞））.
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