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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (12): 25-33.doi: 10.6040/j.issn.1671-9352.0.2021.226

• • 上一篇    

关于两类复微分-差分方程组的超越解

杨祺   

  1. 新疆师范大学数学科学学院, 新疆 乌鲁木齐 830054
  • 发布日期:2022-12-05
  • 作者简介:杨祺(1979— ),女,硕士,副教授,硕士生导师,研究方向为复分析. E-mail:yangqi_8138@126.com
  • 基金资助:
    国家自然科学基金资助项目(11961068)

Transcendental solutions of two types of systems of complex differential-difference equations

YANG Qi   

  1. School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830054, Xinjiang, China
  • Published:2022-12-05

摘要: 利用复差分方程和复微分方程理论,讨论两类复微分-差分方程组的有限级超越整函数解问题,得到两个结果。

关键词: 微分-差分方程, 超越函数, 整函数解

Abstract: By the theory of complex differential equations and complex difference equations,this paper studies transcendental entire solutions with finite order of two types of systems of complex differential-difference equations, and obtains two results.

Key words: differential-difference equation, transcendental function, entire solution

中图分类号: 

  • O174.52
[1] HAYMAN W K. Meromorphic functions[M]. Oxford: Clarendon Press, 1964.
[2] 杨乐. 值分布论及其新研究[M]. 北京: 科学出版社, 1982. YANG Le. Value distribution theory and new researches[M]. Beijing: Science Press, 1982.
[3] 仪洪勋,杨重骏. 亚纯函数唯一性理论[M]. 北京: 科学出版社, 1995. YI Hongxun,YANG Chongjun. Uniqueness theory of meromorphic functions[M]. Beijing: Science Press, 1995.
[4] LAINE I. Nevanlinna theory and complex differential equations[M]. Berlin: Walter de Gruyter, 1993.
[5] YANG Chongjun, LI Ping. On the transcendental solutions of a certain type of nonlinear differential equations[J]. Arch Math, 2004, 82(5):442-448.
[6] LIU Kai, CAO Tingbin, CAO Hongzhe. Entire solutions of Fermat type differential-difference equations[J]. Arch Math, 2012, 99(2):147-155.
[7] CHEN Wei, HU Peichu, ZHANG Yingying. On solutions to some nonlinear difference and differential equations[J]. J Korean Math Soc, 2016, 53(4):835-846.
[8] LIU Kai, YANG Lianzhong. A note on meromorphic solutions of Fermat types equations[J]. An Stiint Univ AI I Cuza Iasi Mat(NS), 2016, 1:317-325.
[9] WANG Qiong, CHEN Wei, HU Peichu. On entire solutions of two certain Fermat-type differential-difference equations[J]. Bull Malays Math Sci Soc, 2020, 43(4):2951-2965.
[10] 高凌云. 两类复微分-差分方程组的整函数解[J]. 数学学报, 2016, 59(5):677-684. GAO Lingyun. Entire solutions of two types of systems of complex differential-difference equations[J]. Acta Mathematics Sinica, 2016, 59(5):677-684.
[11] LIU Manli, GAO Lingyun. On transcendental entire solutions of systems of complex differential-difference equations[J]. Journal of Mathematical Research with Applications, 2017, 37(3):299-306.
[12] 高凌云. 关于一类复微分-差分方程组的解[J]. 数学年刊A辑, 2017, 38(1):23-30. GAO Lingyun. On solutions of a type of systems of complex differential-difference equations[J]. Chinese Annals of Mathematics, Series A, 2017, 38(1):23-30.
[13] GAO Lingyun. On entire solutions of two types of systems of complex differential-difference equations[J]. Acta Math Sci, 2017, 37B(1):187-194.
[14] 刘曼莉,高凌云. 复微分-差分方程组的超越解[J]. 中国科学, 2019, 49(11):1633-1654. LIU Manli, GAO Lingyun. Transcendental solutions of systems of complex differential-difference equations[J]. Scientia Sinica, 2019, 49(11):1633-1654.
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