Existence of Nonoscillatory Solutions for a Third-Order Nonlinear Neutral Delay Differential Equation

The aim of this paper is to study the solvability of a third-order nonlinear neutral delay differential equation of the form {α(t)[β(t)(x(t)+p(t)x(t−τ))′]′}′+f(t,x(σ1(t)),x(σ2(t)),…,x(σn(t)))=0, t≥t0. By using the Krasnoselskii's fixed point theorem and the Schauder's fixed point theorem, we demonstrate the existence of uncountably many bounded nonoscillatory solutions for the above differential equation. Several nontrivial examples are given to illustrate our results.