Existence of nonoscillatory solutions of first-order nonlinear neutral differential equations

Abstract

In this article, we obtain sufficient conditions for first-order nonlinear neutral differential equations to have nonoscillatory solutions for different ranges of p 1 ( t ) and p 2 ( t , ξ ) . We use the Knaster–Tarski fixed point theorem to obtain new sufficient conditions. We give an example to illustrate the applicability of our results.