滨州学院学报
濱州學院學報
빈주학원학보
JOURNAL OF BINZHOU UNIVERSITY
2011年
3期
15-20
,共6页
迭代泛函微分方程%解析解%共振%幂级数
迭代汎函微分方程%解析解%共振%冪級數
질대범함미분방정%해석해%공진%멱급수
iteration functional differential equation%analytic solution%resonance%power series
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.
在複域C內研究瞭一類含有未知函數迭代的二階微分方程的跼部可逆解析解的存在性.通過Schr der變換,把這類方程化為一種不含未知函數迭代的汎函微分方程,併給齣瞭它的跼部可逆解析解.討論瞭雙麯型情形和共振的情形,還在Brjuno條件下討論瞭在共振點附近的情形.
재복역C내연구료일류함유미지함수질대적이계미분방정적국부가역해석해적존재성.통과Schr der변환,파저류방정화위일충불함미지함수질대적범함미분방정,병급출료타적국부가역해석해.토론료쌍곡형정형화공진적정형,환재Brjuno조건하토론료재공진점부근적정형.
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 Schrder 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 Schrder transformation in the hyperbolic case and resonance,but also those near resonance under Brjuno condition.
