Oscillation for a nonlinear dynamic system on time scales

Abstract

We study the oscillation properties of a system of two first-order nonlinear equations on time scales. This form includes the classical Emden-Fowler differential and difference equations and many of its extensions. We generalize some well-known results of Atkinson, Belohorec, Waltman, Hooker, Patula and others and also describe the relation to solutions of a delay-dynamic system.

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

“…However, to the best of our knowledge, there are few results dealing with the oscillation of the solutions of forced dynamic systems on time scales up to now. Motivated by [4,5,11], we will consider the oscillation property of system (1) and establish some oscillation criteria for system (1) in this paper. Our results not only unify the oscillation of twodimensional differential systems and difference systems but also improve the oscillation results that had been established by Saker [9], since our results are not restricted to the case where ( ) ̸ = 0, for all ∈ T and ( ) = .…”