Second-order neutral differential equations: improved criteria for testing the oscillation (Q2034966)

Summary: The main purpose of this study is to establish new improved conditions for testing the oscillation of solutions of second-order neutral differential equation \((r(l) (u'(l))^\gamma)' +q(l) x^\beta (\sigma (l))=0\), where \(l\geq l_0\) and \(u(l):=x(l)+ px(\varrho (l))\). By optimizing the commonly used relationship \(x>(1-p)u\), we obtain new criteria that give sharper results for oscillation than the previous related results. Moreover, we obtain criteria of an iterative nature. Our new results are illustrated by an example.