数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (1): 195-206.doi: 10.1016/S0252-9602(14)60151-X

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MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS

李海绸|高凌云   

  1. Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macau, China  Department of Mathematics, Jinan University, Guangzhou 510632, China
  • 收稿日期:2013-11-29 修回日期:2014-05-14 出版日期:2015-01-20 发布日期:2015-01-20
  • 通讯作者: 李海绸,lihaichou@126.com E-mail:lihaichou@126.com;ylgaojinan@126.com
  • 基金资助:

    The second author is supported by the National Natural Science Foundation of China (10471067) and NSF of Guangdong Province (04010474).

MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS

LI Hai Chou,GAO Ling Yun   

  1. Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macau, China  Department of Mathematics, Jinan University, Guangzhou 510632, China
  • Received:2013-11-29 Revised:2014-05-14 Online:2015-01-20 Published:2015-01-20
  • Contact: LI Hai Chou,lihaichou@126.com E-mail:lihaichou@126.com;ylgaojinan@126.com
  • Supported by:

    The second author is supported by the National Natural Science Foundation of China (10471067) and NSF of Guangdong Province (04010474).

摘要:

Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference equations of the following form

nPj=1 j (z)f
(j1)1 (z + cj ) = R2(z, f2(z)),
n
Pj=1
j (z)f
(j2)
2 (z + cj ) = R1(z, f1(z)).
()
where ij (j = 1, 2, · · · , n; i = 1, 2) are finite non-negative integers, and cj (j = 1, 2, · · · , n) are distinct, nonzero complex numbers, j(z), j(z) (j = 1, 2, · · · , n) are small functions relative to fi(z) (i = 1, 2) respectively, Ri(z, f(z)) (i = 1, 2) are rational in fi(z) (i = 1, 2) with coefficients which are small functions of fi(z) (i = 1, 2) respectively.

关键词: growth order, system of equations, complex differential equations, difference equations, Nevanlinna theory, value distribution

Abstract:

Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference equations of the following form

nPj=1 j (z)f
(j1)1 (z + cj ) = R2(z, f2(z)),
n
Pj=1
j (z)f
(j2)
2 (z + cj ) = R1(z, f1(z)).
()
where ij (j = 1, 2, · · · , n; i = 1, 2) are finite non-negative integers, and cj (j = 1, 2, · · · , n) are distinct, nonzero complex numbers, j(z), j(z) (j = 1, 2, · · · , n) are small functions relative to fi(z) (i = 1, 2) respectively, Ri(z, f(z)) (i = 1, 2) are rational in fi(z) (i = 1, 2) with coefficients which are small functions of fi(z) (i = 1, 2) respectively.

Key words: growth order, system of equations, complex differential equations, difference equations, Nevanlinna theory, value distribution

中图分类号: 

  • 30D05