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Asymptotic behaviour of a difference equation with
complex-valued coefficients

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*Josef Kalas*

**Address.**

Department of Mathematical Analysis,
Faculty of Science, Masaryk University,
Janackovo nam. 2a, 602 00 Brno, Czech Republic

**E-mail. **kalas@math.muni.cz

**Abstract.**

The asymptotic behaviour for solutions of a difference
equation
$\varDelta z_n = f(n,z_n)$,
where the complex-valued function $f(n,z)$ is in some meaning close to
a holomorphic
function $h$, and of a Riccati difference equation is studied
using a Lyapunov function method. The paper is motivated by
papers on the asymptotic behaviour of the solutions of
differential equations with complex-valued right-hand
sides.

**AMSclassification. ** 39A11.

**Keywords. ** Difference equations, asymptotic behaviour, Lyapunov functions.