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Journal of Applied Mathematics
Volume 2013, Article ID 726076, 9 pages
http://dx.doi.org/10.1155/2013/726076
Research Article

Analytic Solutions of an Iterative Functional Differential Equations Near Regular Points

Department of Mathematics, Weifang University, Weifang, Shandong 261061, China

Received 13 August 2012; Accepted 5 March 2013

Academic Editor: Juan Torregrosa

Copyright © 2013 Lingxia Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. Wang, “On the equation x(t)=f(x(x(t))),” Funkcialaj Ekvacioj, vol. 33, no. 3, pp. 405–425, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. Stanck, “On global properties of solutions of functional differential equation x(t)=x(x(t))+x(t),” Dynamic Systems and Applications, vol. 4, pp. 263–278, 1995. View at Google Scholar
  3. J.-G. Si, W.-R. Li, and S. S. Cheng, “Analytic solutions of an iterative functional-differential equation,” Computers & Mathematics with Applications, vol. 33, no. 6, pp. 47–51, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J.-G. Si and S. S. Cheng, “Smooth solutions of a nonhomogeneous iterative functional-differential equation,” Proceedings of the Royal Society of Edinburgh Section A, vol. 128, no. 4, pp. 821–831, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J.-G. Si and X.-P. Wang, “Smooth solutions of a nonhomogeneous iterative functional-differential equation with variable coefficients,” Journal of Mathematical Analysis and Applications, vol. 226, no. 2, pp. 377–392, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J.-G. Si and S. S. Cheng, “Analytic solutions of a functional-differential equation with state dependent argument,” Taiwanese Journal of Mathematics, vol. 1, no. 4, pp. 471–480, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J.-G. Si, X.-P. Wang, and S. S. Cheng, “Analytic solutions of a functional-differential equation with a state derivative dependent delay,” Aequationes Mathematicae, vol. 57, no. 1, pp. 75–86, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. Si and W. Zhang, “Analytic solutions of a nonlinear iterative equation near neutral fixed points and poles,” Journal of Mathematical Analysis and Applications, vol. 284, no. 1, pp. 373–388, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. D. Bjuno, “Analytic form of differential equations,” Transactions of the Moscow Mathematical Society, vol. 25, pp. 131–288, 1971. View at Google Scholar
  10. S. Marmi, P. Moussa, and J.-C. Yoccoz, “The Brjuno functions and their regularity properties,” Communications in Mathematical Physics, vol. 186, no. 2, pp. 265–293, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. T. Carletti and S. Marmi, “Linearization of analytic and non-analytic germs of diffeomorphisms of (,0),” Bulletin de la Société Mathématique de France, vol. 128, no. 1, pp. 69–85, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. A. M. Davie, “The critical function for the semistandard map,” Nonlinearity, vol. 7, no. 1, pp. 219–229, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. D. Bessis, S. Marmi, and G. Turchetti, “On the singularities of divergent majorant series arising from normal form theory,” Rendiconti di Matematica e delle sue Applicazioni, vol. 9, no. 4, pp. 645–659, 1989. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet