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

doi:10.1016/S0252-9602(14)60151-X

Abstract

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

CLC Number:

30D05

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.

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