Oscillatory and asymptotic behaviour 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) for t ∈ [t0,∞]T, where T is a time scale such that sup T = ∞, t0(≥ 0) ∈ T are studied under the assumption ∫ t0∞σ(t)/r(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. Copyright ©2013 Watam Press.