# MEROMORPHIC SOLUTIONS OF SOME q-DIFFERENCE EQUATIONS

• Chen, Baoqin ;
• Chen, Zongxuan
• Published : 2011.11.30
• 42 10

#### 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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#### Cited by

1. FINITE LOGARITHMIC ORDER SOLUTIONS OF LINEAR q-DIFFERENCE EQUATIONS vol.51, pp.1, 2014, https://doi.org/10.4134/BKMS.2014.51.1.083

#### Acknowledgement

Supported by : National Natural Science Foundation of China