Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales

Abstract EN

We will establish a new interval oscillation criterion for second-order half-linear dynamic equation (r(t)[xΔ(t)]α)Δ+p(t)xα(σ(t))=f(t) on a time scale T which is unbounded, which is a extension of the oscillation result for second order linear dynamic equation established by Erbe et al.

(2008).

As an application, we obtain a sufficient condition of oscillation of the second-order half-linear differential equation ([x′(t)]α)′+csintxα(t)=cost, where α=p/q, p, q are odd positive integers.