复微分-差分方程组的整函数解
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摘要
利用值分布理论,研究了一类n阶复微分-差分方程ω~(n)(z)~2+[αω(z+c)-βω(z)]~2=1和复微分-差分方程组■是否存在有限级整函数解的问题.本文推广并改进了高凌云和刘凯等人的结果.
In this paper,using theory of value distribution, we investigate whether a class of order n complex differential-difference equation ω~(n)(z)~2 + [αω(z+c)-βω(z)]~2= 1 and a class of systems of order n complex differential-difference equations ■ have entire solutions with finite order or not. Our results extend and improve the results due to Gao Lingyun and Liu Kai et al.
In this paper,using theory of value distribution, we investigate whether a class of order n complex differential-difference equation ω~(n)(z)~2 + [αω(z+c)-βω(z)]~2= 1 and a class of systems of order n complex differential-difference equations ■ have entire solutions with finite order or not. Our results extend and improve the results due to Gao Lingyun and Liu Kai et al.
引文
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[2]Gao L. Y., Entire solutions of two types of systems of complex differential-difference equations, Acta Math.Sin., Chin. Ser., 2016, 59(5):577-684.
[3]Gross F., On the equation f~n+g~n=1, Bull. Amer. Math. Soc., 1966, 72:86-88.
[4]Halburd R. G., Korhonen R. J., Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl., 2006, 314:477-487.
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[6]Laine I., Rieppo J., Silvennoinen H., Remarks on complex difference equations, Comput. Methods Fanct.Theory, 2005, 5(1):77-88.
[7]Liu K., Cao T. B., Cao H. Z., Entire solutions of Fermat type differential-difference equations, Arch. Math.,2012, 99(5):147-155.
[8]Liu K., Yang L. Z., On entire solutions of some differential-difference equations, Comput. Methods Funct.Theory, 2013, 13(3):433-447.
[9]Yang C. C., Li P., On the transcendental solutions of a certain of nonlinear differential equations, Arch.Math., 2004, 82:442-448.
[10]Yang L., Value Distribution Theory, Springer-Verlag, Berlin, 1993.
[11]Yi H. X., Yang C. C., Theory of the Uniqueness of Meromorphic Function(in Chinese), Science Press,Beijing, 1995.
[2]Gao L. Y., Entire solutions of two types of systems of complex differential-difference equations, Acta Math.Sin., Chin. Ser., 2016, 59(5):577-684.
[3]Gross F., On the equation f~n+g~n=1, Bull. Amer. Math. Soc., 1966, 72:86-88.
[4]Halburd R. G., Korhonen R. J., Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl., 2006, 314:477-487.
[5]Hayman W. K., Meromorphic Functions, Clarendon Press, Oxford, 1964.
[6]Laine I., Rieppo J., Silvennoinen H., Remarks on complex difference equations, Comput. Methods Fanct.Theory, 2005, 5(1):77-88.
[7]Liu K., Cao T. B., Cao H. Z., Entire solutions of Fermat type differential-difference equations, Arch. Math.,2012, 99(5):147-155.
[8]Liu K., Yang L. Z., On entire solutions of some differential-difference equations, Comput. Methods Funct.Theory, 2013, 13(3):433-447.
[9]Yang C. C., Li P., On the transcendental solutions of a certain of nonlinear differential equations, Arch.Math., 2004, 82:442-448.
[10]Yang L., Value Distribution Theory, Springer-Verlag, Berlin, 1993.
[11]Yi H. X., Yang C. C., Theory of the Uniqueness of Meromorphic Function(in Chinese), Science Press,Beijing, 1995.