数学物理学报 ›› 2016, Vol. 36 ›› Issue (2): 297-306.

• 论文 • 上一篇    下一篇

某类非线性微差分方程的整函数解

陈敏风, 高宗升   

  1. 北京航空航天大学LMIB &数学与系统科学学院 北京 100191
  • 收稿日期:2015-09-23 修回日期:2016-01-07 出版日期:2016-04-25 发布日期:2016-04-25
  • 作者简介:陈敏风,chenminfeng198710@126.com;高宗升,zshgao@buaa.edu.cn
  • 基金资助:

    国家自然科学基金(11171013,11371225)资助

Entire Solutions of a Certain Type of Nonlinear Differential-Difference Equation

Chen Minfeng, Gao Zongsheng   

  1. LMIB & School of Mathematics and Systems Science, Beihang University, Beijing 100191
  • Received:2015-09-23 Revised:2016-01-07 Online:2016-04-25 Published:2016-04-25
  • Supported by:

    Supported by the NSFC (11171013, 11371225)

摘要:

该文研究了微差分方程f'(z)2+P(z)2f(z+c)2=Q(z)和f'(z)2+P(z)2(f(z+c)-f(z))2=Q(z),其中P(z)和Q(z)为非零多项式.如果该微差分方程有一个有限级的超越整函数解,那么就可得到这个解的精确表达式.

关键词: 微差分方程, 超越整函数, 有限级

Abstract:

In this paper, we investigate the differential-difference equations f'(z)2+P(z)2f(z+c)2=Q(z) and f'(z)2+P(z)2(f(z+c)-f(z))2=Q(z), where P(z) and Q(z) are nonzero polynomials. If the differential-difference equations admit a transcendental entire solution of finite order, then we can obtain the exact expression of the solution.

Key words: Differential-difference equation, Transcendental entire solution, Finite order

中图分类号: 

  • O175.29