Asymptotic behavior of solutions of a scalar delay difference equations with continuous time

Hajnalka Péics, Andrea Rožnjik

In this work we study the asymptotic behavior of solutions of scalar delay difference equation with continuous time of the form \[ x(t)=a(t)x(t-1)+b(t)x(p(t)), \] where $a$, $b$, $p$ are given real functions such that $p(t)<t$ and $p$ is monotone increasing.