Hille-kneser-type Criteria for Second-order Dynamic Equations on Time Scales

@inproceedings{Erbe2006HilleknesertypeCF,
title={Hille-kneser-type Criteria for Second-order Dynamic Equations on Time Scales},
author={Lynn Erbe and Allan Peterson and Samir H. Saker},
year={2006}
}

We consider the pair of second-order dynamic equations, (r(t)(xΔ)γ)Δ + p(t)xγ(t) = 0 and (r(t)(xΔ)γ)Δ + p(t)xγσ(t) = 0, on a time scale T, where γ > 0 is a quotient of odd positive integers. We establish some necessary and sufficient conditions for nonoscillation of Hille-Kneser type. Our results in the special case when T = R involve the wellknown Hille-Kneser-type criteria of second-order linear differential equations established by Hille. For the case of the second-order half-linear… CONTINUE READING