Acta mathematica scientia, Series B >
MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS
Received date: 2013-11-29
Revised date: 2014-05-14
Online published: 2015-01-20
Supported by
The second author is supported by the National Natural Science Foundation of China (10471067) and NSF of Guangdong Province (04010474).
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.
LI Hai Chou,GAO Ling Yun . MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS[J]. Acta mathematica scientia, Series B, 2015 , 35(1) : 195 -206 . DOI: 10.1016/S0252-9602(14)60151-X
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