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

This paper is concerned with studying the distribution of zeros of solutions of a second-order neutral differential equation of the form (a(t)((x(t)+p(t)x(t-τ))′)γ)′+q(t)f(x(t-σ))=0,when γ≥ 1 and 0 < γ≤ 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.