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中文摘要：
运用上下解方法及不动点指数理论，讨论非齐次边界条件下四阶微分方程四点边值问题{u（4）（t）-f（t,u（t）,u＂（t））=0,t∈[0,1],u（0）=λ1,u（1）=λ2,au＂（ξ1）-bu＇＇＇（ξ1）=-λ3,cu＂（ξ2）＋du＇＇＇（ξ2）=-λ4。得到正解存在的充分条件。给出该非齐次边界条件下，四阶微分方程四点边值问题至少存在一个正解、两个正解及无正解时，参数（λ1，λ2，λ3，λ4）的取值范围。其中：（λ1，λ2，λ3，λ4）∈R4＋＼{（0,0，0，0）}为参数，0≤ξ1≤ξ2≤1，a，b，c,d为非负常数，f∈C（[0，1]×[0，＋∞）×（-∞，0]，[0，＋∞））。
英文摘要：
By using the lower and upper solutions method and fixed point index theory, the sufficient conditions for the existence of positive solutions of the following nonlinear boundary value problem with nonhomogeneous four-point boundary condition are discussed. {u（4）（t）-f（t,u（t）,u＂（t））=0,t∈[0,1],u（0）=λ1,u（1）=λ2,au＂（ξ1）-bu＇＇＇（ξ1）=-λ3,cu＂（ξ2）＋du＇＇＇（ξ2）=-λ4 Where （λ1,λ2,λ3,λ4）∈R4＋／{（0,0,0,0）} are parameters, 0≤ξ1≤ξ2≤1,a,b,c,d are nonnegative constants, f∈C（[0,1]×[0,＋∞）×（-∞,0],[0,＋∞））. The regions of （λ1,λ2,λ3,λ4） , in which the fourth-order differential equation with four-point boundary condition with nonhomogeneous boundary conditions has at least one positive solution, two positive solutions and no positive solution, are determined.
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