## Abstract and Applied Analysis

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

#### 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

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

#### 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