Turkish Journal of Mathematics
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, OLHA; STANZHYTSKYI, OLEKSANDR; and DOBRODZII, TETIANA
(2020)
"The relation between the existence of bounded global solutions of the differential equations and equations on time scales,"
Turkish Journal of Mathematics: Vol. 44:
No.
6, Article 9.
https://doi.org/10.3906/mat-2006-79
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss6/9