利用亚纯函数的Nevanlinna值分布理论,讨论了两类复高阶差分方程亚纯解的存在性和增长级问题,一类复差分方程的Malmquist型定理被建立,另一类复差分方程解的增长级得到估计.例子表明了我们的结果是精确的.
Abstract
In this paper, by Nevanlinna theory of the value distribution of meromorphic functions, we will investigate the problem of the existence and the growth of solutions of two types of complex higher-order difference equations, Malmquist type theorem of one type of difference equations is established, and the growth order of solutions of the other type of complex difference equation is estimated. Some examples show that our results are precise.
关键词
Malmquist型 /
增长级 /
值分布理论 /
复差分方程
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Key words
Malmquist type /
meromorphic solution /
growth order /
complex difference equations
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参考文献
[1] Ablowitz M. J., Halburd R., Herbst B., On the extension of the Painleve property to difference equations, Nonlinearity, 2000, 13(3): 889-905.
[2] Chiang Y. M., Feng S. J., On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions, Trans. Amer. Math. Soc., 2009, 361(7): 3767-3791.
[3] Gao L. Y., Systems of complex difference equations of Malmquist type, Acta Mathematica Sinica, Chinese Series, 2012, 55(2): 293-300.
[4] Halburd R. G., Korhonen R., Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, Journal of Mathematical Analysis and Applications, 2006, 314(2): 477-487.
[5] Heittokangas J., Korhonen R., Laine I., Rieppo J., Tohge K., Complex difference equations of Malmquist type, Computational Methods and Function Theory, 2001, 1(1): 27-39.
[6] Laine I., Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, 1993.
[7] Korhonen R., Meromorphic solutions of differential and difference equations with deficiencies, Ann. Acad. Sci. Fenn., Dissertations, 2002, 129.
[8] Yi H. X., Yang C. C., Theory of the Uniqueness of Meromorphic Functions (in Chinese), Science Press, Beijing, 1995.
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脚注
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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)
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