Second-order neutral differential equations: improved criteria for testing the oscillation
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.
scientific article; zbMATH DE number 7362424