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.