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.

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

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