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http://dx.doi.org/10.4134/BKMS.2011.48.6.1303

MEROMORPHIC SOLUTIONS OF SOME q-DIFFERENCE EQUATIONS  

Chen, Baoqin (School of Mathematical Sciences South China Normal University)
Chen, Zongxuan (School of Mathematical Sciences South China Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.6, 2011 , pp. 1303-1314 More about this Journal
Abstract
We consider meromorphic solutions of q-difference equations of the form $$\sum_{j=o}^{n}a_j(z)f(q^jz)=a_{n+1}(z),$$ where $a_0(z)$, ${\ldots}$, $a_{n+1}(z)$ are meromorphic functions, $a_0(z)a_n(z)$ ≢ 0 and $q{\in}\mathbb{C}$ such that 0 < |q| ${\leq}$ 1. We give a new estimate on the upper bound for the length of the gap in the power series of entire solutions for the case 0 < |q| < 1 and n = 2. Some growth estimates for meromorphic solutions are also given in the cases 0 < |q| < 1. Moreover, we investigate zeros and poles of meromorphic solutions for the case |q| = 1.
Keywords
q-difference equation; growth; type;
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