Oscillatory Behavior of Second-Order Nonlinear Differential Equations with a Nonpositive Neutral Term

We shall present new oscillation criteria of second-order nonlinear differential equations with a nonpositive neutral term of the form: (a(t)x(t)-p(t)x(σ(t))′γ′+q(t)xβ(τ(t))=0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \left( (a(t)\left( \left( x(t)-p(t)x(\sigma (t) )^{\prime } \right) ^{\gamma } \right) ^{\prime }+q(t)x^{\beta }(\tau (t))=0,\right. \end{aligned}$$\end{document}with positive coefficients. The obtained results answer an open problem raised in Li et al. [Adv Differ Equ 35:7, 2015, Remark 4.3 (P2)]. Examples are given to illustrate the main results.