Oscillation theorems for second-order superlinear neutral differential equations

Abstract

Abstract The purpose of this paper is to investigate the oscillation of the second-order neutral differential equations of the form (E)$$ (r(t)|z'(t)|^{\alpha - 1} z'(t))' + q(t)|x(\sigma (t))|^{\alpha - 1} x(\sigma (t)) = 0, $$ where z(t) = x(t) + p(t)x(τ(t)). The obtained comparison principles essentially simplify the examination of the studied equations. Further, our results extend and improve the results in the literature.