Existence of nonoscillatory solutions for a third-order nonlinear neutral delay differential equation (Q638137)

The authors study the solvability of a third-order nonlinear neutral delay differential equation of the form \[ (\alpha(t)(\beta(t)(x(t)+p(t)x(t-\tau))')')'+f(t,x(\sigma_1(t)),x(\sigma_2(t)),\dots,x(\sigma_n(t)))=0,\;t\geq t_0. \] By using Krasnosel'skii's fixed-point theorem and Schauder's fixed-point theorem, they demonstrate the existence of uncountably many bounded nonoscillatory solutions for the above equation. Several nontrivial examples are given to illustrate the obtained results.