Olha KARPENKO, Oleksandr STANZHYTSKYI, Tetiana DOBRODZII

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

This work is devoted to the study of existence of a bounded solution of the differential equation, defined on a family of time scales Tλ , provided the graininess function µλ converges to zero as λ → 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.

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