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Existence of an analytic solution for a first order iterative functional differential equation

LIU Ling-xia   

  1. School of Mathematics and Information Science, Weifang University, Weifang 261061, Shandong, China
  • Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
  • Contact: LIU Ling-xia

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Abstract: The existence of an analytic solution was discussed for a first order iterative functional differential equation x′(z)=1/x(az+bx(z)), z∈C （Ⅰ） in a complex field. In previous work［6］, the eigen-value of the linearization was required to fulfill that α is not on the unit circle or lies on the circle with the Diophantine condition. Results of the analytic solution were obtained in the case that α was the unit root and the case that α is near resonance under the Brjuno condition.

Key words: majorant series , analytic solution, iterative

CLC Number: 

  • O193
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