Growth of meromorphic solutions of linear difference equations
نویسندگان
چکیده
منابع مشابه
On meromorphic solutions of certain type of difference equations
We mainly discuss the existence of meromorphic (entire) solutions of certain type of non-linear difference equation of the form: $f(z)^m+P(z)f(z+c)^n=Q(z)$, which is a supplement of previous results in [K. Liu, L. Z. Yang and X. L. Liu, Existence of entire solutions of nonlinear difference equations, Czechoslovak Math. J. 61 (2011), no. 2, 565--576, and X. G. Qi...
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and Applied Analysis 3 where |q| > 1 and the index set J consists of m elements and the coefficients a i (z) (a n (z) = 1) and b J (z) are small functions of f. If f is of finite order, then |q| < n + m − 1. 2. Some Lemmas The following important result by Valiron andMohon’ko will be used frequently, one can find the proof in Laine’s book [16, page 29]. Lemma 9. Let f be a meromorphic function....
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Abstract. In this paper, we investigate the higher-order linear differential equations with meromorphic coefficients. We improve and extend a result of M.S. Liu and C.L. Yuan, by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen, and the extended Winman-Valiron theory which proved by J. Wang and H.X. Yi. In addition, we also consider th...
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we mainly discuss the existence of meromorphic (entire) solutions of certain type of non-linear difference equation of the form: $f(z)^m+p(z)f(z+c)^n=q(z)$, which is a supplement of previous results in [k. liu, l. z. yang and x. l. liu, existence of entire solutions of nonlinear difference equations, czechoslovak math. j. 61 (2011), no. 2, 565--576, and x. g. qi...
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In this paper, we give some necessary conditions for a complex difference equation of Malmquist type $$sum^n_{j=1}f(z+c_j)=frac{P(f(z))}{Q(f(z))},$$ where $n(in{mathbb{N}})geq{2}$, and $P(f(z))$ and $Q(f(z))$ are relatively prime polynomials in $f(z)$ with small functions as coefficients, admitting a meromorphic function of finite order. Moreover, the properties of finite o...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2011
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2011.05.069