On the relation between oscillation of solutions of differential equations and corresponding equations on time scales

Authors

OLEXANDR STANZHYTSKYI
ROZA UTESHOVA
VICTORIIA TSAN
ZOIA KHALETSKA

Abstract

This paper studies oscillatory properties of solutions of a dynamic equation on the set of time scales $\mathbf{T}_\lambda$ provided that the graininess function $\mu_\lambda$ approaches zero as $\lambda\to 0$. We derived the conditions under which oscillation of solutions of differential equations implies that of solutions of the corresponding equations defined on time scales with the same initial data, and vice versa.

DOI

10.55730/1300-0098.3373

Keywords

Time scale, graininess function, oscillation, $\Delta-$derivative, generalized zero

First Page

476

Last Page

501

Recommended Citation

STANZHYTSKYI, OLEXANDR; UTESHOVA, ROZA; TSAN, VICTORIIA; and KHALETSKA, ZOIA (2023) "On the relation between oscillation of solutions of differential equations and corresponding equations on time scales," Turkish Journal of Mathematics: Vol. 47: No. 2, Article 5. https://doi.org/10.55730/1300-0098.3373
Available at: https://journals.tubitak.gov.tr/math/vol47/iss2/5