Oscillation of Second-Order Forced Nonlinear Dynamic Equations on Time Scales.

In this paper, we discuss the oscillatory behavior of the second-order forced nonlinear dynamic equation (a(t)xΔ(t))+p(t)f(xο)=r(t), on a time scale T when a(t) > 0. We establish some sufficient conditions which ensure that every solution oscillates or satisfies lim inft→∞ |x(t)| = 0. Our oscillation results when r(t) = 0 improve the oscillation results for dynamic equations on time scales that has been established by Erbe and Peterson [Proc. Amer. Math. Soc 132 (2004), 735-744], Bohner, Erbe and Peterson [J. Math. Anal. Appl. 301 (2005), 491-507] since our results do not require ∫∞t0 q(t)Δt > 0 and ∫±∞± t0 du/f(u) < ∞. Also, as a special case when T = R, and r(t) = 0 our results improve some oscillation results for differential equations. Some examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]