growth of meromorphic solutions for complex difference equations of malmquist type
Authors
abstract
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 order transcendental meromorphic solutions for complex difference equation $prod^n_{j=1}f(z+c_j)=p(f(z))/q(f(z))$ are also investigated.
similar resources
Growth of meromorphic solutions for complex difference equations of Malmquist type
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...
full textOn 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...
full texton 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...
full textGrowth of Meromorphic Solutions of Some q-Difference Equations
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....
full textSome Properties of Meromorphic Solutions of Systems of Complex q-Shift Difference Equations
and Applied Analysis 3 The coefficients {ci ki (z)}, {di ti (z)} are meromorphic functions and small functions, S (r) = ∑T (r, a (i) ) +∑T(r, b (j) )
full textNevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations
It is shown that, if f is a meromorphic function of order zero and q ∈ C, then m „ r, f(qz) f(z) « = o(T (r, f)) (‡) for all r on a set of logarithmic density 1. The remainder of the paper consist of applications of identity (‡) to the study of value distribution of zero-order meromorphic functions, and, in particular, zero-order meromorphic solutions of q-difference equations. The results obta...
full textMy Resources
Save resource for easier access later
Journal title:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۶، صفحات ۱۴۹۷-۱۵۰۵
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023