Malmquist型复差分方程组

高凌云

数学学报 ›› 2012 ›› Issue (2) : 293-300.

PDF(225 KB)
中国科学院数学与系统科学研究院期刊网
PDF(225 KB)
数学学报 ›› 2012 ›› Issue (2) : 293-300. DOI: 10.12386/A2012sxxb0029
论文

Malmquist型复差分方程组

    高凌云
作者信息 +

Systems of Complex Di erence Equations of Malmquist Type

    Ling Yun GAO
Author information +
文章历史 +

摘要

近来一些论文里,Ablowitz,Halburd 以及 Herbst等人应用Nevanlinna理论证明了类似于复微分方程Malmquist定理的复差分方程一些结果.本文主要研究一类复差分方程组的Malmquist定理,推广和改进了他们的一些结论.

Abstract

In recent papers, Ablowitz, Halburd and Herbst et al. applied Nevanlinna theory to prove some results on complex di erence equations reminiscent of the classical Malmquist theorem in complex di erential equations. We will mainly investigate Malmquist theorem of a type of systems of complex di erence equations; improvements and extensions of such results are presented in this paper.

关键词

Malmquist 型 / 亚纯解 / 值分布理论 / 复差分方程

Key words

Malmquist type / meromorphic solution / value distribution / complex difference equations

引用本文

EndNote

Ris (Procite)

Bibtex

导出引用
高凌云. Malmquist型复差分方程组. 数学学报, 2012(2): 293-300 https://doi.org/10.12386/A2012sxxb0029
Ling Yun GAO. Systems of Complex Di erence Equations of Malmquist Type. Acta Mathematica Sinica, Chinese Series, 2012(2): 293-300 https://doi.org/10.12386/A2012sxxb0029

参考文献

[1] Yi H. X., Yang C. C., Theory of the Uniqueness of Meromorphic Functions, Beijing: Science Press, 1995 (in Chinese).

[2] Laine I., Nevanlinna Theory and Complex Di erential Equations, Berlin: Walter de Gruyter, 1993.

[3] Ablowitz M. J., Halburd R., Herbst B., On the extension of the Painleve property to di erence equations, Nonlinearity, 2000, 13(3): 889-905.

[4] Bergweiler W., Langley J. K., Zeros of di erences of meromorphic functions, Mathematical Proceedings of the Cambridge Philosophical Society, 2007, 142(1): 133-147.

[5] Chiang Y. M., Feng S. J., On the Nevanlinna characteristic of f(z + η) and di erence equations in the complex plane, Ramanujan Journal, 2008, 16(1): 105-129.

[6] Gundersen G. G., Heittokangas J. etc., Meromorphic solutions of generalized Schroder, Aequationes Mathe-maticae, 2002, 63(1/2): 110-135.

[7] Heittokangas J., Korhonen R., Laine I., Rieppo J., Tohge K., Complex di erence equations of Malmquist type, Computational Methods and Function Theory, 2001, 1(1): 27-39.

[8] Halburd R. G., Korhonen R., Di erence analogue of the lemma on the logarithmic derivative with applications to di erence equations, Journal of Mathematical Analysis and Applications, 2006, 314(2): 477-487.

[9] Halburd R. G., Korhonen R., Nevanlinna theory for the difference operator, Annales Academia Scientiarium Fennica. Mathematica, 2006, 31(2): 463-478.

[10] Halburd R. G., Korhonen R., Existence of nite-order meromorphic solutions as a detector of integrability in di erence equations, Physica D, 2006, 218(2): 191-203.

[11] Ishizaki K., Yanagihara N., Wiman-Valiron method for di erence equations, Nagoya Mathematical Journal, 2004, 175: 75-102.

[12] Laine I., Rieppo J., Silvennoinen H., Remarks on complex di erence equations, Computational Methods and Function Theory, 2005, 5(1): 77-88.

[13] Gromak V., Laine I., Shimomura S., Painleve Di erential Equations in the Complex Plane, Vol. 28 of Studies in Mathematics, de Gruyter, New York, NY, USA, 2002.

[14] Weissenborn G., On the theorem of Tumura and Clunie, The Bulletin of the London Mathematical Society, 1986, 18(4): 371-373.

[15] Bergweiler W., Langley J. K., Zeros of di erences of meromorphic functions, Math. Proc. Camb. Philos. Soc., 2007, 142(1): 133-147.

[16] Chiang Y. M., Ruijsenaars S. N. M., On the Nevanlinna order of meromorphic solutions to linear analytic di erence equations, Stud. Appl. Math., 2006, 116: 257-287.

[17] Ruijsenaars S. N. M., First order analytic di erence equations and integrable quantum systems. J. Math. Phys., 1997, 40: 1069-1146.

[18] Korhonen R., A new Clunie type theorem for di erence polynomials, J. Di erence Equ. Appl., 2011, 17(3): 387-400.

基金

国家自然科学基金资助项目(10471065);广东省自然科学基金资助项目(04010474)

PDF(225 KB)

233

Accesses

0

Citation

Detail
段落导航
相关文章

/

〈 〉