Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales - Quanwen Lin; Baoguo Jia; Qiru Wang (Abstract and Applied Analysis)
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)=cos⁡t, where α=p/q, p, q are odd positive integers.