Existence of nonoscillatory solutions of second-order differential equations with mixed neutral term

In this study, we aim to contribute to the increasing interest in functional differential equations by obtaining new existence theorems for non-oscillatory solutions of second-order neutral differential equations involving positive and negative terms which have not been performed in previous studies. We consider different cases for the ranges of the neutral coefficients, by utilizing the Banach contraction mapping principle. The applicability of the results is illustrated by several examples in the last section.