一类二阶迭代泛函微分方程的局部可逆解析解  

Local Invertible Analytic Solutions of a Second-order Iterative Functional Differential Equation

作　　者：朱先军[1] 

机构地区：[1]济宁学院数学系,山东曲阜273155

出　　处：《滨州学院学报》2011年第3期15-20,共6页Journal of Binzhou University

基　　金：山东省高等学校科技计划项目(J10LA55);济宁学院科研基金项目(2010KJLX06)

摘　　要：在复域C内研究了一类含有未知函数迭代的二阶微分方程的局部可逆解析解的存在性.通过Schr der变换,把这类方程化为一种不含未知函数迭代的泛函微分方程,并给出了它的局部可逆解析解.讨论了双曲型情形和共振的情形,还在Brjuno条件下讨论了在共振点附近的情形.The second-order differential equation involving iterates of the unknown function is studied in the complex field C for the existence of local invertible analytic solutions.By using the Schrder transformation,we transform this equation into another functional differential equation without iteration of the unknown function,and give its local invertible analytic solutions.We discuss not only those given in the Schrder transformation in the hyperbolic case and resonance,but also those near resonance under Brjuno condition.

关 键 词：迭代泛函微分方程 解析解 共振 幂级数 

分 类 号：O175.12[理学—数学]