LOCAL ANALYTIC SOLUTIONS OF A MORE GENERALIZED DHOMBRES EQUATION  

作　　者：张倩 

机构地区：[1]School of Science,Southwest University of Science and Technology

出　　处：《Acta Mathematica Scientia》2013年第1期207-217,共11页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundation of China(11101295)

摘　　要：We study the local analytic solutions f of the functional equation f（ψ（zf（z））） = φ（f（z）） for z in some neighborhood of the origin. Whether the solution f vanishes at z = 0 or not plays a critical role for local analytic solutions of this equation. In this paper, we obtain results of analytic solutions not only in the case f（0） = 0 but also for f（0） ≠ 0. When assuming f（0） = 0, for technical reasons, we just get the result for f′（0）≠ 0. Then when assuming f（0） = ω0 ≠ 0, ψ（0） = s # 0, ψ（z） is analytic at z = 0 and ψ（z） is analytic at z = ω0, we give the existence of local analytic solutions f in the case of 0 〈 ｜sω0｜ 〈 1 and the case of ｜sω0｜ = 1 with the Brjuno condition.We study the local analytic solutions f of the functional equation f（ψ（zf（z））） = φ（f（z）） for z in some neighborhood of the origin. Whether the solution f vanishes at z = 0 or not plays a critical role for local analytic solutions of this equation. In this paper, we obtain results of analytic solutions not only in the case f（0） = 0 but also for f（0） ≠ 0. When assuming f（0） = 0, for technical reasons, we just get the result for f′（0）≠ 0. Then when assuming f（0） = ω0 ≠ 0, ψ（0） = s # 0, ψ（z） is analytic at z = 0 and ψ（z） is analytic at z = ω0, we give the existence of local analytic solutions f in the case of 0 〈 ｜sω0｜ 〈 1 and the case of ｜sω0｜ = 1 with the Brjuno condition.

关 键 词：local analytic solutions the majorant series functional equation Brjunocondition 

分 类 号：O241.8[理学—计算数学]