- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 634739, 8 pages
Complex Oscillation of Higher-Order Linear Differential Equations with Coefficients Being Lacunary Series of Finite Iterated Order
1College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China
2Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen, Jiangxi 333403, China
3School of Sciences, Jiangxi Agricultural University, Nanchang 330045, China
4Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, China
5Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, 80101 Joensuu, Finland
Received 18 January 2013; Accepted 12 April 2013
Academic Editor: Micah Osilike
Copyright © 2013 Jin Tu et al. 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.
- W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, UK, 1964.
- I. Laine, Nevanlinna Theory and Complex Differential Equations, vol. 15, Walter de Gruyter, Berlin, Germany, 1993.
- C.-C. Yang and H.-X. Yi, Uniqueness Theory of Meromorphic Functions, vol. 557, Kluwer Academic, Dordrecht, The Netherlands, 2003.
- B. Belaïdi, “Growth and oscillation of solutions to linear differential equations with entire coefficients having the same order,” Electronic Journal of Differential Equations, no. 70, pp. 1–10, 2009.
- B. Belaidi, “On the iterated order and the fixed points of entire solutions of some complex linear differential equations,” Electronic Journal of Qualitative Theory of Differential Equations, no. 9, pp. 1–11, 2006.
- L. G. Bernal, “On growth k-order of solutions of a complex homogeneous linear differential equation,” Proceedings of the American Mathematical Society, vol. 101, no. 2, pp. 317–322, 1987.
- T. Cao and H. Yi, “On the complex oscillation of higher order linear differential equations with meromorphic coefficients,” Journal of Systems Science & Complexity, vol. 20, no. 1, pp. 135–148, 2007.
- L. Kinnunen, “Linear differential equations with solutions of finite iterated order,” Southeast Asian Bulletin of Mathematics, vol. 22, no. 4, pp. 385–405, 1998.
- J. Tu and Z.-X. Chen, “Growth of solutions of complex differential equations with meromorphic coefficients of finite iterated order,” Southeast Asian Bulletin of Mathematics, vol. 33, no. 1, pp. 153–164, 2009.
- J. Tu and T. Long, “Oscillation of complex high order linear differential equations with coefficients of finite iterated order,” Electronic Journal of Qualitative Theory of Differential Equations, no. 66, pp. 1–13, 2009.
- Y.-M. Chiang and W. K. Hayman, “Estimates on the growth of meromorphic solutions of linear differential equations,” Commentarii Mathematici Helvetici, vol. 79, no. 3, pp. 451–470, 2004.
- J. Tu and G. T. Deng, “Growth of solutions to higher-order linear differential equations with the coefficient A0 being dominant,” Acta Mathematica Scientia A, vol. 30, no. 4, pp. 945–952, 2010.
- Z.-X. Chen and C.-C. Yang, “Quantitative estimations on the zeros and growths of entire solutions of linear differential equations,” Complex Variables, vol. 42, no. 2, pp. 119–133, 2000.
- I. Laine and P. C. Wu, “Growth of solutions of second order linear differential equations,” Proceedings of the American Mathematical Society, vol. 128, no. 9, pp. 2693–2703, 2000.
- J. Tu and J. Liu, “Growth of solutions of a class of higher order linear differential equations with coefficients being gap series,” Journal of Mathematical Research and Exposition, vol. 29, no. 3, pp. 563–567, 2009.
- J. Tu and G. Deng, “Growth of solutions of certain higher order linear differential equations,” Complex Variables and Elliptic Equations, vol. 53, no. 7, pp. 623–631, 2008.
- G. G. Gundersen, “Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates,” Journal of the London Mathematical Society, vol. 37, no. 1, pp. 88–104, 1988.
- T. Kövari, “A gap-theorem for entire functions of infinite order,” The Michigan Mathematical Journal, vol. 12, pp. 133–140, 1965.
- H. Hu and X. M. Zheng, “Growth of solutions to linear differential equations with entire coefficients,” Electronic Journal of Differential Equations, no. 226, pp. 1–15, 2012.
- W. K. Hayman, “The local growth of power series: a survey of the Wiman-Valiron method,” Canadian Mathematical Bulletin, vol. 17, no. 3, pp. 317–358, 1974.