On the Relationship Between Solutions of Boundary Value Problems for Differential Equations and Corresponding Problems for Dynamic Equations on Time Scales

ABSTRACT This paper investigates the relationship between solutions of boundary value problems for ordinary differential equations and those for a family of dynamic equations on time scales. The main result demonstrates that, when the graininess tends to zero, the solvability of the problem for the family of dynamic equations ensures the solvability of its continuous counterpart. The opposite result is also established.