Asymptotic behaviour of a difference equation with complex-valued coefficients

Josef Kalas

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


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.