On oscillatory and asymptotic behavior of fourth order non-linear neutral delay dynamic equations

Abstract

In this paper, oscillatory and asymptotic property of solutions of a class of nonlinear fourth order neutral dynamic equations of the form (H)( r(t)(y(t)+p(t)y(α(t)))Δ2) Δ2+q(t)G(y(β(t)))=0 and (NH)(r(t)(y(t)+p(t) y(α(t)))Δ2)Δ2+q(t)G(y(β(t)))=f(t) fort∈[t0,∞]T,t00, where T is a time scale such that sup T=∞, t0∈T have been studied under the assumption ∫t0∞tr(t)Δt=∞ for various ranges of p(t). Sufficient conditions are obtained for the existence of bounded positive solutions of (NH) by using Schauder's fixed point theorem. © 2011 Elsevier Ltd. All rights reserved.