Most results on the polynomial-like iterative equation are given under the condition that the given function is monotone, while a work by L. Liu and X. Gong gets non-monotone PM solutions with height 1 when the given function is of the same case. Removing the condition on height for the given function, we first give a method to assert the nonexistence of C 0 solutions, then present equivalent conditions for the existence of PM solutions with finite height. Finally, as an application of the equivalent conditions, we construct the PM solutions in the case that the given function has one fort.

中文翻译：

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类多项式迭代方程的广义结果

类多项式迭代方程的大部分结果是在给定函数是单调的条件下给出的，而L. Liu和X. Gong的工作在给定函数是相同的情况下得到高度为1的非单调PM解. 去除给定函数的高度条件，我们首先给出一种方法来断言 C 0 解不存在，然后给出具有有限高度的 PM 解存在的等价条件。最后，作为等价条件的应用，我们构造了给定函数有一个堡垒的情况下的PM解。