关于差分Riccati方程及时滞微分方程的相关结果

数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 832-838.

关于差分Riccati方程及时滞微分方程的相关结果

王琼¹(),龙芳²(),王珺^3,*()

¹ 山东大学数学学院济南 250100
² 江西省机械高级技工学校南昌 330013
³ 复旦大学数学科学学院上海 200433

收稿日期:2018-05-14 出版日期:2019-08-26 发布日期:2019-09-11
通讯作者: 王珺 E-mail:qiongwangsdu@126.com;969356135@qq.com;majwang@fudan.edu.cn
作者简介:王琼, E-mail:qiongwangsdu@126.com|龙芳, E-mail:969356135@qq.com
基金资助:
国家自然科学基金(11771090);国家自然科学基金(11571049);国家自然科学基金(11271227);国家自然科学基金(11461070);上海自然科学基金(17ZR1402900);教育部长江学者和创新团队发展计划项目(IRT1264);山东大学基本科研业务费专项资金(2017JC019)

Some Results on Difference Riccati Equations and Delay Differential Equations

Qiong Wang¹(),Fang Long²(),Jun Wang^3,*()

¹ Department of Mathematics, Shandong University, Jinan 250100
² Jiangxi Vocational College of Mechanical and Electrical Technology, Nanchang 330013
³ School of Mathematical Sciences, Fudan University, Shanghai 200433

Received:2018-05-14 Online:2019-08-26 Published:2019-09-11
Contact: Jun Wang E-mail:qiongwangsdu@126.com;969356135@qq.com;majwang@fudan.edu.cn
Supported by:
the NSFC(11771090);the NSFC(11571049);the NSFC(11271227);the NSFC(11461070);the Natural Science Foundation of Shanghai(17ZR1402900);the PCSIRT(IRT1264);the Fundamental Research Funds of Shandong University(2017JC019)

摘要/Abstract

摘要：

研究了有理系数的差分Riccati方程和常系数的时滞微分方程.当系数满足一定关系时，证明了差分Riccati方程的超越亚纯解具有不小于1的增长级.对于常系数的时滞微分方程，讨论了有理解在z → ∞时的渐近行为.

关键词: 差分Riccati方程, 亚纯解, 时滞微分方程, 有理解

Abstract:

We investigate difference Riccati equations with rational coefficients and delay differential equations with constant coefficients. For difference Riccati equations with some relation among coefficients, we prove that every transcendental meromorphic solution is of order no less than one. We also consider the rational solutions for delay differential equations.

Key words: Difference Riccati equation, Meromorphic solution, Delay differential equation, Rational solution

中图分类号:

O174.52

王琼,龙芳,王珺. 关于差分Riccati方程及时滞微分方程的相关结果[J]. 数学物理学报, 2019, 39(4): 832-838.

Qiong Wang,Fang Long,Jun Wang. Some Results on Difference Riccati Equations and Delay Differential Equations[J]. Acta mathematica scientia,Series A, 2019, 39(4): 832-838.

参考文献

1	Ablowitz M J , Halburd R , Herbst B . On the extension of the Painlevé property to difference equations. Nonlinearity, 2000, 13 (3): 889- 905
2	Chen Z X . Zeros of entire solutions to complex linear difference equations. Acta Mathematica Scientia, 2012, 32 (3): 1141- 1148
3	Chen Z X . On growth, zeros and poles of meromorphic solutions of linear and nonlinear difference equations. Science China Math, 2011, 54 (10): 2123- 2133
4	Chen Z X . Complex Differences and Difference Equations. Beijing: Science Press, 2014
5	Chiang Y M , Feng S J . On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane. Ramanujan J, 2008, 16 (1): 105- 129
6	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 (2): 477- 487
7	Halburd R G , Korhonen R J . Existence of finite-order meromorphic solutions as a detector of integrability in difference equations. Physica D, 2006, 218: 191- 203
8	Halburd R G , Korhonen R J . Growth of meromorphic solutions of delay differential equation. Proc Amer Math Soc, 2017, 145 (6): 2513- 2526
9	Halburd R G , Korhonen R J . Nevanlinna theory for the difference operator. Ann Acad Sci Fenn Math, 2006, 31 (2): 463- 478
10	Halburd R G , Korhonen R J . Meromorphic solutions of difference equations, integrability and the discrete Painlevé equations. J Phys, 2007, 40 (6): 1- 38
11	Ishizaki K . On difference Riccati equations and second order linear difference equations. Aequationes Mathematicae, 2011, 81 (1): 185- 198
12	Laine I. Nevanlinna Theory and Complex Differential Equations. Berlin:Walter de Gruyter, 1993
13	Nevanlinna R, Behnke H, Grauert H, et al. Analytic Functions. New York:Springer-Verlag, 1970
14	Quispel G R W , Capel H W , Sahadevan R . Continuous symmetries of differential difference equations:the Kac-van Moerbeke equation and Painlevé reduction. Phys Lett A, 1992, 170 (5): 379- 383
15	Yang C C , Yi H X . Uniqueness Theory of Meromorphic Functions. Dordrecht: Kluwer Academic Publishers, 2004

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