Existence of positive periodic solutions to third-order delay differential equations

Abstract

Using the continuation theorem of coincidence degree theory and analysis techniques, we establish criteria for the existence of periodic solutions to the following third-order neutral delay functional differential equation with deviating arguments x˙˙˙(t) + aẍ(t) + g(ẋ(t - τ(t))) + ƒ(x(t - τ(t))) = p(t). Our results complement and extend known results and are illustrated with examples.