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On growth, zeros and poles of meromorphic solutions of linear and nonlinear difference equations. (English) Zbl 1238.30019

The author studies the order of growth, zeros and poles of finite order meromorphic solutions of nonlinear difference equations

$P\left(z\right)y\left(z+1\right)y\left(z\right)+Q\left(z\right)y\left(z\right)y\left(z-1\right)=H\left(z\right)\phantom{\rule{2.em}{0ex}}\left(1·1\right)$

and

$y\left(z+1\right)=\frac{R\left(z\right)y\left(z\right)}{Q\left(z\right)+P\left(z\right)y\left(z\right)},\phantom{\rule{2.em}{0ex}}\left(1·2\right)$

where $P\left(z\right),Q\left(z\right),H\left(z\right)$ and $R\left(z\right)$ are polynomials such that $P\left(z\right)Q\left(z\right)H\left(z\right)R\left(z\right)¬\equiv 0$. Similar results for linear difference equations related to (1.1) and (1.2) are also obtained.

##### MSC:
 30D35 Distribution of values (one complex variable); Nevanlinna theory 39A10 Additive difference equations
##### References:
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