Oscillation results for fourth-order nonlinear neutral dynamic equations

Abstract

In this paper, the authors study the oscillatory and asymptotic properties of solutions of nonlinear fourth order neutral dynamic equations of the form (r(t)(y(t)+ p(t)y(α(t)))δ2)δ2 +q(t)G(y(β(t)))-h(t)H(γ((t))) = 0 (H) and (r(t)(y(t)+ p(t)y(α(t))) δ2) δ2 +q(t)G(y(β(t))) -h(t)H(γ((t))) = f (t), (NH) where T is a time scale with supT = ∞, t ∈ [t0,1)T, and t0 > 0. They assume that ∫ t0∞σ(t) r(t) δt < ∞ and obtain results for various ranges of values of p(t). Examples illustrating the results are included. © 2013 Project Euclid.