- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 619296, 6 pages
On Growth of Meromorphic Solutions for Linear Difference Equations
1School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
2Department of Mathematics, College of Natural Sciences, Pusan National University, Pusan 609-735, Republic of Korea
Received 9 June 2013; Accepted 19 August 2013
Academic Editor: Norio Yoshida
Copyright © 2013 Zong-Xuan Chen and Kwang Ho Shon. 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.
- Z. Chen, “On growth, zeros and poles of meromorphic solutions of linear and nonlinear difference equations,” Science China, vol. 54, no. 10, pp. 2123–2133, 2011.
- Z.-X. Chen, “Growth and zeros of meromorphic solution of some linear difference equations,” Journal of Mathematical Analysis and Applications, vol. 373, no. 1, pp. 235–241, 2011.
- Y.-M. Chiang and S.-J. Feng, “On the Nevanlinna characteristic of and difference equations in the complex plane,” Ramanujan Journal, vol. 16, no. 1, pp. 105–129, 2008.
- K. Ishizaki, “On difference Riccati equations and second order linear difference equations,” Aequationes Mathematicae, vol. 81, no. 1-2, pp. 185–198, 2011.
- K. Ishizaki and N. Yanagihara, “Wiman-Valiron method for difference equations,” Nagoya Mathematical Journal, vol. 175, pp. 75–102, 2004.
- I. Laine and C.-C. Yang, “Clunie theorems for difference and -difference polynomials,” Journal of the London Mathematical Society. Second Series, vol. 76, no. 3, pp. 556–566, 2007.
- S. Li and Z.-S. Gao, “Finite order meromorphic solutions of linear difference equations,” Proceedings of the Japan Academy Series A, vol. 87, no. 5, pp. 73–76, 2011.
- X.-M. Zheng and J. Tu, “Growth of meromorphic solutions of linear difference equations,” Journal of Mathematical Analysis and Applications, vol. 384, no. 2, pp. 349–356, 2011.
- W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, UK, 1964.
- I. Laine, Nevanlinna Theory and Complex Differential Equations, vol. 15 of de Gruyter Studies in Mathematics, Walter de Gruyter & Co., Berlin, Germany, 1993.
- W. K. Hayman, “Slowly growing integral and subharmonic functions,” Commentarii Mathematici Helvetici, vol. 34, pp. 75–84, 1960.
- W. Bergweiler and J. K. Langley, “Zeros of differences of meromorphic functions,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 142, no. 1, pp. 133–147, 2007.
- R. G. Halburd and R. J. Korhonen, “Difference analogue of the lemma on the logarithmic derivative with applications to difference equations,” Journal of Mathematical Analysis and Applications, vol. 314, no. 2, pp. 477–487, 2006.