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

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,t0⩾0, where TT is a time scale such that sup T=∞T=∞, t0∈Tt0∈T have been studied under the assumption ∫t0∞tr(t)Δt=∞ for various ranges of p(t)p(t). Sufficient conditions are obtained for the existence of bounded positive solutions of (NH)(NH) by using Schauder’s fixed point theorem.