一类迭代方程扩张解的存在性

Existence of expansive solutions for an iterative equation

作者讨论了一类广泛的迭代方程f^n(x)=G(x,f(x),f^2(x),…,f^(h-1)(x)).通过Sch(o|¨)rder变换,迭代方程被转化为辅助方程的形式.在不要求方程中含有f^1的条件下作者给出了局部C^1解的存在性.它的特殊形式就是多项式型迭代方程的首项系数问题.

A general kind of iterative equation f^n（x）=G（x,f（x）,f^2（x）,..,f^n-1 （x）） is discussed. The equation is reduced to an auxiliary equation by Schroder transformation, and the local C1 solution is given without the hypothesis that f^1 exists. Its special form is the leading coefficient problem of polynomial-like iterative equations.