On the differential and difference equation with a power delayed argument

J. Cermák, Technical University of Brno, Brno, Czech Republic

E. J. Qualitative Theory of Diff. Equ., Proc. 8'th Coll. Qualitative Theory of Diff. Equ., No. 5. (2008), pp. 1-8.

Abstract: We study the qualitative behaviour of solutions of the differential equation
$$
\dot{y}(t)=a\,y(t^{\alpha})+b\,y(t),\qquad t\in [1,\infty ),
$$
where $0<\alpha <1$, $a\ne 0$, $b\le 0$ are real scalars. Our aim is to present (and using the analysis of the numerical discretization also partly explain) some specific properties of solutions on the unbounded as well as the compact domain.

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