Oscillation theorems for second-order neutral functional dynamic equations on time scales

Abstract

In this article, we obtain several comparison theorems for the second-order neutral dynamic equation $$ Big(r(t)ig([x(t)+p(t)x(au(t))]^Deltaig)^gammaBig)^Delta +q_1(t)x^lambda(delta(t))+q_2(t)x^eta(eta(t))=0, $$ where $gamma,lambda, eta$ are ratios of positive odd integers. We compare such equation with the first-order dynamic inequalities in the sense that the absence of the eventually positive solutions of these first-order inequalities implies the oscillation of the studied equation.

Keywords

• Oscillation
• neutral functional dynamic equation
• comparison theorem
• time scales