Oscillatory Behaviour of a First-Order Neutral Differential Equation in relation to an Old Open Problem

Abstract EN

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht

Further, each rjt, gt, and ht⟶∞ as t⟶∞.

This paper improves and generalizes some known results.