Oscillation of higher order nonlinear dynamic equations on time scales

Abstract

Some new criteria for the oscillation of nth order nonlinear dynamic equations of the form xΔn(t) + q (t) (xσ (ξ (t))) λ = 0 are established in delay ξ(t) ≤ t and non-delay ξ(t) = t cases, where n ≥ 2 is a positive integer, l is the ratio of positive odd integers. Many of the results are new for the corresponding higher order difference equations and differential equations are as special cases. © 2012 Grace et al.