On the correspondence between periodic solutions of differential and dynamic equations on periodic time scales (Q6620613)

This discusses the relationship between the existence of periodic solutions of dynamic equations on time scales and that of corresponding differential equations. There are two main results in this paper. The first one provides the condition for the existence of a periodic solution of the system of differential equations when the corresponding system of dynamic equations has a periodic solution. The next result is the converse of the first one. In fact, it establishes the existence of a periodic solution of the system of dynamic equations when the system of corresponding differential equations has a periodic solution. Both the results are established on a time scale with sufficiently small graininess. As an illustration, the obtained results are applied to the van der Pol differential equation, which serves as a mathematical model for a lamp-driven oscillator and describes its oscillations of electric current. The behaviour of the solutions of these equations is presented graphically.