On The Iterated Exponent of Convergence of Solutions of Linear Differential Equations

Main Article Content



In this paper, we investigate the relationship between solutions and their derivatives of the differential equation f^{(k)}+A_{k-1}f^{(k-1)}+...+A₀f=0 for k≥2 and small functions, where A_{j} (j=0,1,...,k-1) are meromorphic functions of finite iterated p-order.

Article Details


  1. B. Bela ¨idi, Oscillation of fixed points of solutions of some linear differential equations, Acta. Math. Univ. Comenianae, 77 (2008), 263-269.
  2. L. G. Bernal, On growth k-order of solutions of a complex homogeneous linear differential equation, Proceedings of the American Mathematical Society, 101 (1987), 317-322.
  3. R. Bouabdelli and B. Bela ¨idi, On the iterated exponent of convergence of solutions of linear differential equations with entire and meromorphic coefficients, Journal of Mathematics, 2013 (2013), Article ID 429083.
  4. Z. X. Chen, The fixed points and hyper-order of solutions of second order complex differential equations, Acta Mathematica Scientia, 20 (2000), 425-432. (in Chinese).
  5. T. B. Cao, Z. X. Chen, X. M. Zheng, and J. Tu, On the iterated order of meromorphic solutions of higher order linear differential equations, Annals of Differential Equations, 21 (2005), 111-122.
  6. A. El Farissi, and M. Benbachir, Oscillation of fixed points of solutions to complex linear differential equations, Electron. J. Diff. Equ., 2013 (2013), Article ID 41.
  7. A. El Farissi, Value Distribution of Meromorphic Solutions and their Derivatives of Complex Differential Equations, Hindawi publishing corporation, ISRN Mathematical Analysis, 2013 (2013), Article ID 497921.
  8. G. G. Gundersen, Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J. London Math. Soc., 2 (1988), 88-104.
  9. W. K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964
  10. L. Kinnunen, Linear differential equations with solutions of finite iterated order, Southeast Asian Bull. Math., 22 (1998), 385-405.
  11. I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, New York, 1993.
  12. M. S. Liu and X. M. Zhang, Fixed points of meromorphic solutions of higher order Linear differential equations, Ann. Acad. Sci. Fenn. Ser. A. I. Math., 31 (2006), 191-211.
  13. R. Nevanlinna, Eindeutige analytische Funktionen, Zweite Auflage. Reprint. Die Grundlehren der mathematischen Wissenschaften, Band 46. Springer-Verlag, Berlin-New York, 1974.
  14. J. Wang and W. R. L ¨u, The fixed points and hyper-order of solutions of second order linear differential equations with meromorphic coefficients, Acta Math. Appl. Sin. 27 (2004), 72-80. (in Chinese).
  15. H. Y. Xu, J. Tu, X. M. Zheng, On the hyper exponent of convergence of zeros of f (j) - φ of higher order linear differential equations, Advances in Difference Equations, 2012 (2012), article 114.
  16. H. X. Yi and C. C. Yang, The Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, 1995 (in Chinese).
  17. Q. T. Zhang and C. C. Yang, The Fixed Points and Resolution Theory of Meromorphic Functions, Beijing University Press, Beijing, 1988 (in Chinese).