Abstract
In a recent papers,some authors applied Nevanlinna theory to prove some results on complex difference equations reminiscent of the classical Malmquist theorem in complex differential equations. We will mainly investigate Malmquist theorem of a type of systems of complex partial difference equations on C n, improvements and extensions of such results are presented in this paper.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ablowitz, M.J., Halburd, R.. Herbst, B. On the extension of the Painlevé property to difference equations. Nonlinearity, 13(3): 889–905 (2000)
Bergweiler, W., Langley, J.K. Zeros of differences of meromorphic functions. Math. Proc. Camb. Phil. Soc., 142(1): 133–147 (2007)
Biancofiore, A., Stoll, W. Another proof of the lemma of the logarithmic derivative in several complex variables. In: Recent developments in several complex variables, p.29–45, Ann. Math. Stud., Vol.100, Princeton University Press, New Jersey, 1981
Chiang, Y.M., Feng, S.J. On the Nevanlinna characteristic of f(z + η) and difference equations in the complex plane. Ramanujan Journal, 16(1): 105–129 (2008)
Chiang, Y.M., Ruijsenaars, S.N.M. On the Nevanlinna order of meromorphic solutions to linear analytic difference equations. Stud. Appl. Math., 116: 257–287 (2006)
Gao Lingyun. On admissible solution of two types of systems of complex differential equations. Acta Math. Sinica, 43(1): 149–156 (2000)
Gundersen, G.G., Heittokangas, J., etc. Meromorphic solutions of generalized Schroder. Aequationes Mathematicae, 63(1–2): 110–135 (2002)
Halburd, R.G., Korhonen, R.J. Difference analogue of the lemma on the logarithmic derivative with applications to difference equations. Journal of Mathematical Analysis and Applications, 314(2): 477–487 (2006)
Halburd, R.G., Korhonen, R.J. Nevanlinna theory for the difference operator. Annales Academia Scientiarium Fennica Mathematica, 31(2): 463–478 (2006)
Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J., Tohge, K. Complex difference equations of Malmquist type. Computational Methods and Function Theory, 1(1): 27–39 (2001)
Ishizaki, K., Yanagihara, N. Wiman-Valiron method for difference equations. Nagoya Mathematical Journal, 175: 75–102 (2004)
Korhonen, R.A. Difference Picard theorem for meromorphic functions of several variables. Computational Methods and Function Theory, 12(1): 343–361 (2012)
Laine, I. Nevanlinna theory and complex differential equations. Walter de Gruyter, Berlin, 1993
Laine, I., Rieppo, J. Silvennoinen, H. Remarks on complex difference equations. Computational Methods and Function Theory, 5(1): 77–88 (2005)
Tu Zhenhan. Some Malmquist type theorems of partial differential equations on Cn. J. of Math. Anal. and Appl., 179: 41–60 (1993)
Yi Hongxun, Yang C C. Theory of the uniqueness of meromorphic functions. Science Press, Beijing, 1995 (in Chinese)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China (No.10471065) and the Natural Science Foundation of Guangdong Province (No.04010474).
Rights and permissions
About this article
Cite this article
Gao, Ly., Zheng, Zm. Admissible solutions of systems of complex partial difference equations on Cn . Acta Math. Appl. Sin. Engl. Ser. 31, 297–306 (2015). https://doi.org/10.1007/s10255-015-0470-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10255-015-0470-8