AN APPLICATION OF DYNAMIC SYSTEMS ON TIME SCALES WITH INITIAL TIME DIFFERENCE INVOLVING A COMPARISON RESULT AND LYAPUNOV STABILITY

摘要

We investigate the qualitative behavior of a perturbed dynamic systems on time scales that differs in initial position and initial time with respect to the unperturbed dynamic systems on time scales. We compare the classical notion of stability to the notion of initial time difference stability on time scales. We present a comparison result which again gives the null solution a central role in the comparison dynamic systems on time scales when establishing initial time difference stability of the perturbed dynamic systems on time scales with respect to the unperturbed dynamic systems on time scales.