Oscillation for a Nonlinear Dynamic System with a Forced Term on Time Scales

Abstract

We consider a class of two-dimensional nonlinear dynamic system with a forced term on a time scale T and obtain sufficient conditions for all solutions of the system to be oscillatory. Our results not only unify the oscillation of two-dimensional differential systems and difference systems but also improve the oscillation results that have been established by Saker, 2005, since our results are not restricted to the case where ( ) ̸ = 0 for all ∈ T and ( ) = . Some examples are given to illustrate the results.

Oscillation Criteria of Two-Dimensional Time-Scale Systems

“…Oscillation criteria for Eq. 16, system (17), and other similar versions of (15) and (17) are investigated in [39][40][41][42]. A solution x; y ðÞ of system (15) is called oscillatory if x and y have arbitrarily large zeros.…”

On Oscillation of Two-Dimensional Time-Scale Systems with a Forcing Term

“…and for some variations of systems (1) and (3) are shown in [14,15,18,22]. A solution (x, y) of system (1) is called oscillatory if x and y have arbitrarily large zeros.…”