New Oscillation Criteria for Higher Order Nonlinear Dynamic Equations

Abstract

This paper deals with some new criteria for the oscillation of higher-order nonlinear dynamic equations with mixed deviating arguments. The purpose of the present paper is the linearization of the equation under consideration. Specifically, we will infer the oscillation of the studied equation from its linear form and establish new oscillation criteria by comparing it with first-order equations whose oscillatory behaviour is known. The obtained results are new, improve, and correlate many of the known oscillation criteria appearing in the literature. The results are illustrated by two examples.