The relation between the existence of bounded global solutions of the differential equations and equations on time scales

Authors

OLHA KARPENKO
OLEKSANDR STANZHYTSKYI
TETIANA DOBRODZII

Abstract

This work is devoted to the study of existence of a bounded solution of the differential equation, defined on a family of time scales $\mathbb{T}_\lambda$, provided the graininess function $\mu_\lambda$ converges to zero as $\lambda\to 0$. We obtained the conditions, under which the existence of a bounded solution of differential equation implies the existence of a bounded solution of the corresponding equation, defined on time scales, and vice versa.

DOI

10.3906/mat-2006-79

Keywords

Time scale, differential equation, asymptotic stability, graininess function, bounded solution

First Page

2099

Last Page

2112

Recommended Citation

KARPENKO, O, STANZHYTSKYI, O, & DOBRODZII, T (2020). The relation between the existence of bounded global solutions of the differential equations and equations on time scales. Turkish Journal of Mathematics 44 (6): 2099-2112. https://doi.org/10.3906/mat-2006-79