Oscillation of fourth-order nonlinear neutral delay dynamic equations

Abstract

In this work we establish some new sufficient conditions for oscillation of fourth-order nonlinear neutral delay dynamic equations of the form (a(t)([x(t) − p(t)x(h(t))] ∆∆∆) α) ∆ + q(t)x β (g(t)) = 0, t ∈ [t0, ∞) T , where α and β are quotients of positive odd integers with β ≤ α.

OSCILLATION THEOREMS FOR FOURTH-ORDER NONLINEAR DYNAMIC EQUATIONS ON TIME SCALES Vol. 3(2) July 2015, No. 4, pp. 46-58 F. Z. LADRANI, A.HAMMOUDI, A. BENAISSA CHERIF

“…It's clear that the form of problem ( 1) is more general than all the problems considered in [8], [9] and [11].…”

“…Erbe et al [6] investigated a third-order dynamic equation with a half-linear damping x ∆ 3 (t) + q (t) x (t) = 0. Said R. Grace et al [8] studied oscillation of the fourth-order dynamic equations…”

A Survey of Recent Results for the Generalizations of Ordinary Differential Equations

“…Periodic solutions were investigated in [36]. OscillationS of solutions have been considered in [37][38][39] using the time scales Taylor formula, [40][41][42][43][44][45]. Asymptotic behavior of solutions has been studied in [46,47] using Taylor monomials and in [47].…”

Oscillation Criteria for Fourth-Order Nonlinear Dynamic Equations on Time Scales

“…on a time scale T, where 𝛾 is the ratio of odd positive integers, 𝑝 is a positive real-valued rd-continuous function defined on T, 𝜏 ∈ 𝐶 rd (T, T), 𝜏(𝑡) ≤ 𝑡, and lim 𝑡 → ∞ 𝜏(𝑡) = ∞. Grace et al in [17] were concerned with the oscillation of the fourth-order nonlinear dynamic equation…”