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Existence of analytic solutions of a second-iterative functional differential equation

LIU Ling-xia   

  1. The Mathematics Departments, 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: Analytic solutions of a secondorder iterative functional differential equation x″(x［r］(z))=c0z+c1x(z)+…+cmx［m］(z), z∈C, were discussed in a complex field, where r and m　are nonnegative integers, c0,c1,…,cm　are complex constants, and x［i］　is the ith iterated function x(z). The analytic solutions are obtained in the case of unit root α， of which that the linearized eigenvalue α is near resonance under the Brjuno condition.

Key words: majorant series , analytic solution, functional differential equation, iteration

CLC Number: 

  • O175
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