"New asymptotic results for half-linear differential equations with deviating argument"

Abstract

"In the paper, we study the oscillation of the half-linear second-order differential equations with deviating argument of the form \begin{equation*} \left(r(t)(y'(t))^{\alpha}\right)'=p(t)y^{\alpha}(\tau(t)). \tag{$E$} \end{equation*} We introduce new monotonic properties of nonoscillatory solutions and use them to offer new criteria for elimination of certain types of solutions. The presented results essentially improve existing ones even for linear differential equations."