JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (12): 25-33.doi: 10.6040/j.issn.1671-9352.0.2021.226

Previous Articles    

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

PDF (PC)

278

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

CLC Number: 

  • 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.
[1] ZHANG Wei-jie, WANG Xin-li, WANG Han-jie. Uniqueness of differential polynomials of meromorphic functions IM sharing a value [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 90-96.
[2] GU Yong-yi, KONG Yin-ying. Meromorphic solutions of a class of auxiliary differential equation and its applications [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 81-89.
[3] LIU Man-li, GAO Ling-yun. Meromorphic solutions of a type of system of complex difference equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(10): 34-40.
[4] ZHANG Guo-wei. Radial distribution of Julia sets of derivatives of solutions to complex differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 85-88.
[5] QU Jing-jing . Uniqueness of meromorphic functions that share one IM value [J]. J4, 2006, 41(2): 54-58 .
[6] XU Jun-feng and ZHANG Zhan-liang . Derivatives of meromorphic functions concerning fix-points and polynomials [J]. J4, 2007, 42(5): 1-04 .
[7] QU Jing-jing . Uniqueness of meromorphic functions with their derivatives [J]. J4, 2007, 42(10): 22-26 .
[8] XU Rong-xia and WANG Ji-chao . Meromorphic functions sharing a finite set [J]. J4, 2007, 42(5): 5-08 .
[9] ZHANG Ji-long and YI Hong-xun . The uniqueness of function derivative that share one CM value [J]. J4, 2006, 41(1): 115-119 .
[10] ZHANG Ji-long . The uniqueness of differential polynomials sharing common values [J]. J4, 2007, 42(6): 61-64 .
[11] BIE Rong-jun and WANG Xin-li . Uniqueness theorems of meromorphic functions concerning three shared sets [J]. J4, 2007, 42(8): 30-35 .
[12] CAO Yin-hong,GAO Rui . A unicity theorem on the entire function and its linear differential polynomials [J]. J4, 2007, 42(12): 69-72 .
[13] CHEN Wei1, YUAN Wen-jun2, TIAN Hong-gen1*. A note on a result due to Yang Le and Schwick [J]. J4, 2013, 48(10): 90-93.
[14] SHI Xin-hua. Uniqueness of meromorphic functions and differential polynomials sharing two values IM [J]. J4, 2013, 48(10): 82-85.
[15] WANG Ling-shuang, HUANG Zhi-gang. Uniqueness of meromorphic solutions of nonlinear differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 106-114.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd