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

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 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.