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

Abstract and Applied Analysis

Research Article

Lianzhong Yang¹  Jian Wang²  Guowei Zhang² 

[1] School of Mathematics, Shandong University, Jinan, Shandong 250100, China, sdu.edu.cn;School of Mathematics and Statistics, Anyang Normal University, Anyang, Henan 455000, China, aynu.edu.cn

Others  :  1320798
DOI  :  10.1155/2014/842693

 received in 2014-03-06, accepted in 2014-05-12,  发布年份 2014

【 摘 要 】

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.

【 授权许可】

CC BY   
Copyright © 2014 Guowei Zhang et al. 2014

【 参考文献 】

• [1]A. A. Goldberg, I. V. Ostrovskii. (2008). Value Distribution of Meromorphic Functions.236. DOI: 10.1090/S0273-0979-1993-00432-4.
• [2]W. K. Hayman. (1964). Meromorphic Functions. DOI: 10.1090/S0273-0979-1993-00432-4.
• [3]I. Laine. (1993). Nevanlinna Theory and Complex Differential Equations.15. DOI: 10.1090/S0273-0979-1993-00432-4.
• [4]L. Yang. (1993). Value Distribution Theory. DOI: 10.1090/S0273-0979-1993-00432-4.
• [5]C.-C. Yang, H.-X. Yi. (2003). Uniqueness Theory of Meromorphic Functions.557. DOI: 10.1090/S0273-0979-1993-00432-4.
• [6]W. Bergweiler. (1993). Iteration of meromorphic functions. Bulletin of the American Mathematical Society.29(2):151-188. DOI: 10.1090/S0273-0979-1993-00432-4.
• [7]J. H. Zheng. (2006). Dynamics of Meromorphic Functions. DOI: 10.1090/S0273-0979-1993-00432-4.
• [8]I. N. Baker. (1965). Sets of non-normality in iteration theory. Journal of the London Mathematical Society.40:499-502. DOI: 10.1090/S0273-0979-1993-00432-4.
• [9]J. Qiao. (1994). Julia set of entire functions and their derivatives. Chinese Science Bulletin.39(3):186-188. DOI: 10.1090/S0273-0979-1993-00432-4.
• [10]J. Y. Qiao. (1994). Stable sets for iterations of entire functions. Acta Mathematica Sinica.37(5):702-708. DOI: 10.1090/S0273-0979-1993-00432-4.
• [11]J. Qiao. (2001). On limiting directions of Julia sets. Annales Academiæ Scientiarum Fennicæ.26(2):391-399. DOI: 10.1090/S0273-0979-1993-00432-4.
• [12]L. Qiu, S. Wu. (2006). Radial distributions of Julia sets of meromorphic functions. Journal of the Australian Mathematical Society.81(3):363-368. DOI: 10.1090/S0273-0979-1993-00432-4.
• [13]S. Wang. (2007). On radial distribution of Julia sets of meromorphic functions. Taiwanese Journal of Mathematics.11(5):1301-1313. DOI: 10.1090/S0273-0979-1993-00432-4.
• [14]J.-H. Zheng, S. Wang, Z.-G. Huang. (2002). Some properties of Fatou and Julia sets of transcendental meromorphic functions. Bulletin of the Australian Mathematical Society.66(1):1-8. DOI: 10.1090/S0273-0979-1993-00432-4.
• [15]Z. Huang, J. Wang. (2012). On the radial distribution of Julia sets of entire solutions of. Journal of Mathematical Analysis and Applications.387(2):1106-1113. DOI: 10.1090/S0273-0979-1993-00432-4.
• [16]Z.-G. Huang, J. Wang. (2014). On limit directions of Julia sets of entire solutions of linear differential equations. Journal of Mathematical Analysis and Applications.409(1):478-484. DOI: 10.1090/S0273-0979-1993-00432-4.
• [17]P. Wu, J. Zhu. (2011). On the growth of solutions to the complex differential equation. Science China.54(5):939-947. DOI: 10.1090/S0273-0979-1993-00432-4.
• [18]P. D. Barry. (1970). Some theorems related to the theorem. Proceedings of the London Mathematical Society.21:334-360. DOI: 10.1090/S0273-0979-1993-00432-4.
• [19]I. N. Baker. (1975). The domains of normality of an entire function. Annales Academiæ Scientiarum Fennicæ.1(2):277-283. DOI: 10.1090/S0273-0979-1993-00432-4.