Abstract and Applied Analysis

On Radial Distribution of Julia Sets of Solutions to Certain Second Order Complex Linear Differential Equations

Guowei Zhang, Jian Wang, and Lianzhong Yang

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We mainly investigate the radial distribution of the Julia set of entire solutions to a special second order complex linear differential equation, one of the entire coefficients of which has a finite deficient value.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 842693, 6 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277014

Digital Object Identifier
doi:10.1155/2014/842693

Mathematical Reviews number (MathSciNet)
MR3216079

Zentralblatt MATH identifier
07023182

Citation

Zhang, Guowei; Wang, Jian; Yang, Lianzhong. On Radial Distribution of Julia Sets of Solutions to Certain Second Order Complex Linear Differential Equations. Abstr. Appl. Anal. 2014 (2014), Article ID 842693, 6 pages. doi:10.1155/2014/842693. https://projecteuclid.org/euclid.aaa/1412277014


Export citation

References

  • A. A. Goldberg and I. V. Ostrovskii, Value Distribution of Meromorphic Functions, vol. 236 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, USA, 2008.
  • W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, UK, 1964.
  • I. Laine, Nevanlinna Theory and Complex Differential Equations, vol. 15 of de Gruyter Studies in Mathematics, Walter de Gruyter, Berlin, Germany, 1993.
  • L. Yang, Value Distribution Theory, Springer, Berlin, Germany, 1993.
  • C.-C. Yang and H.-X. Yi, Uniqueness Theory of Meromorphic Functions, vol. 557 of Mathematics and Its Applications, Science Press, Beijing, China; Kluwer Academic Publishers, Dodrecht, The Netherlands, 2003.
  • W. Bergweiler, “Iteration of meromorphic functions,” Bulletin of the American Mathematical Society, vol. 29, no. 2, pp. 151–188, 1993.
  • J. H. Zheng, Dynamics of Meromorphic Functions, Tsinghua University Press, Beijing, China, 2006, (Chinese).
  • I. N. Baker, “Sets of non-normality in iteration theory,” Journal of the London Mathematical Society, vol. 40, pp. 499–502, 1965.
  • J. Qiao, “Julia set of entire functions and their derivatives,” Chinese Science Bulletin, vol. 39, no. 3, pp. 186–188, 1994.
  • J. Y. Qiao, “Stable sets for iterations of entire functions,” Acta Mathematica Sinica, vol. 37, no. 5, pp. 702–708, 1994 (Chinese).
  • J. Qiao, “On limiting directions of Julia sets,” Annales Academiæ Scientiarum Fennicæ, vol. 26, no. 2, pp. 391–399, 2001.
  • L. Qiu and S. Wu, “Radial distributions of Julia sets of meromorphic functions,” Journal of the Australian Mathematical Society, vol. 81, no. 3, pp. 363–368, 2006.
  • S. Wang, “On radial distribution of Julia sets of meromorphic functions,” Taiwanese Journal of Mathematics, vol. 11, no. 5, pp. 1301–1313, 2007.
  • J.-H. Zheng, S. Wang, and Z.-G. Huang, “Some properties of Fatou and Julia sets of transcendental meromorphic functions,” Bulletin of the Australian Mathematical Society, vol. 66, no. 1, pp. 1–8, 2002.
  • Z. Huang and J. Wang, “On the radial distribution of Julia sets of entire solutions of ${f}^{(n)}+A(z)f=0$,” Journal of Mathematical Analysis and Applications, vol. 387, no. 2, pp. 1106–1113, 2012.
  • Z.-G. Huang and J. Wang, “On limit directions of Julia sets of entire solutions of linear differential equations,” Journal of Mathematical Analysis and Applications, vol. 409, no. 1, pp. 478–484, 2014.
  • P. Wu and J. Zhu, “On the growth of solutions to the complex differential equation ${f}^{\prime \prime }+A{f}^{\prime }+Bf=0$,” Science China, vol. 54, no. 5, pp. 939–947, 2011.
  • P. D. Barry, “Some theorems related to the $\text{cos}\pi \rho $ theorem,” Proceedings of the London Mathematical Society, vol. 21, pp. 334–360, 1970.
  • I. N. Baker, “The domains of normality of an entire function,” Annales Academiæ Scientiarum Fennicæ, vol. 1, no. 2, pp. 277–283, 1975. \endinput