Distribution of zeros of second order superlinear and sublinear neutral delay differential equations

Abstract

This paper is concerned with studying the distribution of zeros of solutions of a second-order neutral differential equation of the form $$\begin{aligned} \left( a\left( t\right) \left( \left( x(t)+p\left( t\right) x\left( t-\tau \right) \right) ^{^{\prime }}\right) ^{\gamma }\right) ^{^{\prime }}+q(t)f\left( x(t-\sigma )\right) =0, \end{aligned}$$ when $$\gamma \ge 1$$ and $$0<\gamma \le 1$$ . The results extend and partially improve the results obtained in Li et al. (Appl Math Lett 63:14–20, 2017). The results will be obtained by employing a technique based on a specific sequence of functions which contains the coefficients of the equation. Two examples are given to illustrate the main results.