Acta mathematica scientia, Series B >
ON PROPERTIES OF MEROMORPHIC SOLUTIONS FOR COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE
Received date: 2012-03-25
Online published: 2013-07-20
Supported by
This project was supported by the National Natural Science Foundation of China (11171119)
In this paper, we present the properties on zeros, fixed points, poles, Borel exceptional value of finite order transcendental meromorphic solutions of complex difference
equation of Malmquist type
∑nj=1f (z + cj ) = R(f (z)) =P(f (z))Q(f (z))=apf(z)p + ap−1f (z)p−1 + … + a1f (z) + a0/bqf (z)q + bq−1f (z)q−1 + … + b1f(z) + b0,
where n(∈ N) ≥ 2, P(f(z)) and Q(f(z)) are relatively prime polynomials in f(z) with rational coefficients as (s = 0, 1, … , p) and bt (t = 0, 1, … , q) such that a0apbq 6≡ 0, and also consider the existence and the forms on rational solutions of this type of difference equations. Some examples are also listed to show that the assumptions of theorems, in certain senses, are the best possible.
Key words： zeros; poles; fixed-points; Borel exceptional value; difference equation
HUANG Zhi-Bo , CHEN Zong-Xuan , LI Qian . ON PROPERTIES OF MEROMORPHIC SOLUTIONS FOR COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE[J]. Acta mathematica scientia, Series B, 2013 , 33(4) : 1141 -1152 . DOI: 10.1016/S0252-9602(13)60070-3
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