《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
杨祺
YANG Qi
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。
中图分类号:
[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] | 张伟杰,王新利,王汉杰. 亚纯函数微分多项式IM分担值的唯一性[J]. 《山东大学学报(理学版)》, 2019, 54(8): 90-96. |
[2] | 古勇毅,孔荫莹. 一类辅助微分方程的亚纯解及其应用[J]. 《山东大学学报(理学版)》, 2019, 54(8): 81-89. |
[3] | 刘曼莉,高凌云. 一类复差分方程组的亚纯解[J]. 山东大学学报(理学版), 2016, 51(10): 34-40. |
[4] | 张国威. 复微分方程解的导数的Julia集的径向分布[J]. 山东大学学报(理学版), 2016, 51(2): 85-88. |
[5] | 曲静静 . 分享1 IM的亚纯函数惟一性[J]. J4, 2006, 41(2): 54-58 . |
[6] | 徐俊峰,张占亮 . 与不动点和多项式有关的亚纯函数导数的零点[J]. J4, 2007, 42(5): 1-04 . |
[7] | 曲静静 . 亚纯函数及其导数的惟一性[J]. J4, 2007, 42(10): 22-26 . |
[8] | 许荣霞,王际朝 . 亚纯函数具有有限公共值集问题[J]. J4, 2007, 42(5): 5-08 . |
[9] | 张继龙,仪洪勋 . 函数导数分担1个公共值的惟一性[J]. J4, 2006, 41(1): 115-119 . |
[10] | 张继龙 . 微分多项式分担公共值的惟一性[J]. J4, 2007, 42(6): 61-64 . |
[11] | 别荣军,王新利 . 具有分担三个值集的亚纯函数的惟一性[J]. J4, 2007, 42(8): 30-35 . |
[12] | 曹银红,高 瑞 . 关于整函数与其微分多项式的惟一性定理[J]. J4, 2007, 42(12): 69-72 . |
[13] | 陈玮1,袁文俊2,田宏根1*. 关于杨乐及Schwick的一个结果的注记[J]. J4, 2013, 48(10): 90-93. |
[14] | 石新华. 亚纯函数微分多项式IM分担两个值的惟一性[J]. J4, 2013, 48(10): 82-85. |
[15] | 王凌霜,黄志刚. 非线性微分方程解的唯一性[J]. 《山东大学学报(理学版)》, 2019, 54(12): 106-114. |
|