Oscillation and Asymptotic Behaviour of a Higher-Order Nonlinear Neutral-Type Functional Differential Equation with Oscillating Coefficients

Abstract

We will study oscillation of bounded solutions of higher-order nonlinear neutral delay differential equations of the following type:[y(t)+p(t)f(y(τ(t)))](n)+q(t)h(y(σ(t)))=0,t≥t0,t∈R, wherep∈C([t0,∞),R),limt→∞p(t)=0,q∈C([t0,∞),R+),τ(t),σ(t)∈C([t0,∞),R),τ(t),σ(t)<t,lim⁡t→∞τ(t),σ(t)=∞, andf,h∈C(R,R). We obtain sufficient conditions for the oscillation of all solutions of this equation.