On oscillatory first order nonlinear neutral differential equations with nonlinear impulses

Abstract

In this work, we study the oscillatory behaviour of solutions of a class of first order impulsive neutral delay differential equations of the form

$$\begin{aligned} {\left\{ \begin{array}{ll} \bigl (y(t)-p(t)y(t-\tau )\bigr )' + q(t)G\bigl (y(t-\sigma )\bigr )=0,\;t\ne t_k,\;t \ge t_0 \\ y(t^+_k)=I_k\bigl (y(t_k)\bigr ), \;k \in {\mathbb {N}} \\ y(t^+_k-\tau )=I_k\bigl (y(t_k-\tau )\bigr ), \;k \in {\mathbb {N}} \end{array}\right. } \end{aligned}$$

for different ranges of the neutral coefficient p. Finally, two illustrative examples are included to show the effectiveness and feasibility of the main results.