Oscillation for Higher Order Dynamic Equations on Time Scales

Abstract EN

We investigate the oscillation of the following higher order dynamic equation: {an(t)[(an-1(t)(⋯(a1(t)xΔ(t))Δ⋯)Δ)Δ]α}Δ+p(t)xβ(t)=0, on some time scale T, where n≥2, ak(t) (1≤k≤n) and p(t) are positive rd-continuous functions on T and α,β are the quotient of odd positive integers.

We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.