Necessary and sufficient conditions for oscillation of nonlinear first-order forced differential equations with several delays of neutral type

In this work, necessary and sufficient conditions are obtained such that every solution of nonlinear neutral first-order differential equations with several delays of the form (Equation presented) is oscillatory or tends to zero as t → ∞. This problem is considered in various ranges of the neutral coefficient r. Finally, some illustrating examples are presented to show that feasibility and effectiveness of main results. © 2019 Walter de Gruyter GmbH, Berlin/Boston 2019.