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.

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

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