一类具有二阶导数的广义迭代微分方程的解析解

讨论一类具有二阶导数的广义非线性迭代方程．通过Schrsder变换将其化为它的辅助方程，利用优级数证明其局部解析解的存在性，并根据SchrtMer变换中参数卢的不同情况进行讨论．不仅讨论一般的情况，而且讨论临界情况，特别是当β是单位根时，此类方程在迭代理论和应用方面都有重要意义．

Analytic solution for a generalized iterative equation with second - order derivatives

A generalized nonlinear iterative equation with secondorder derivatives is considered. By reducing the equation with Schrtider transformation to the other functional equation, we prove the existence of its local analytic solutions based on the means of majorant series, and discuss the different cases that the parameterβ given in the Schrtider transformation. We discuss not only the general case, but also the critical cases as well, especially for thatβ is a unit root, such equation is important in both applications and the theory of iteration.