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中文摘要：
通过使用Hammastein积分方程和锥上的不动点定理对于一类含时间奇异性的二阶非线性Dirich．1et问题建立了三个局部存在定理．主要结论表明只要非线性项的主要部分在某些有界集合上的高度是适当的此问题具有n个正解，其中竹是一个任意的自然数．
英文摘要：
Three local existence theorems are established for a second-order nonlinear Dirichlet problem with time singularity by using Hammastein integral equation and fixed point theorem on cone. Main results show that the problem has n positive solutions provided the heights of principal part of nonlinear term on some bounded sets are appropriate, where n is an arbitrary positive integer.
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