Commun. Korean Math. Soc. 2017; 32(4): 959-970
Printed October 31, 2017
https://doi.org/10.4134/CKMS.c170004
Copyright © The Korean Mathematical Society.
Zong Sheng Gao, Xiao Ming Wang
Beihang University, Beihang University
In this paper, we investigate the transcendental meromorphic solutions with finite order of two different types of difference equations \begin{align*} \sum_{j=1}^{n}a_jf(z+c_j)=\frac{P(z,f)}{Q(z,f)}=\frac{\sum_{k=0}^{p}b_kf^k}{\sum_{l=0}^{q}d_lf^l} \end{align*} and \begin{align*} \prod_{j=1}^{n}f(z+c_j)=\frac{P(z,f)}{Q(z,f)}=\frac{\sum_{k=0}^{p}b_kf^k}{\sum_{l=0}^{q}d_lf^l} \end{align*} that share three distinct values with another meromorphic function. Here $a_j$, $b_k$, $d_l$ are small functions of $f$ and $a_j\not\equiv 0(j=1,2,\ldots,n)$, $b_p\not\equiv 0$, $d_q\not\equiv 0$. $c_j\neq 0$ are pairwise distinct constants. $p$, $q$, $n$ are non-negative integers. $P(z,f)$ and $Q(z,f)$ are two mutually prime polynomials in $f$.
Keywords: uniqueness, meromorphic solution, difference equations
MSC numbers: 30D35, 34M05, 39A10
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