Asymptotic Properties of Third-Order Delay Trinomial Differential Equations

Abstract

The aim of this paper is to study properties of the third-order delay trinomial differential equation ${\left(\right(1/r\left(t\right)\left)y^{\prime \prime }\right(t\left)\right)}^{\prime }+p\left(t\right)y^{\prime }\left(t\right)+q\left(t\right)y\left(\sigma \right(t\left)\right)=0$, by transforming this equation onto the second-/third-order binomial differential equation. Using suitable comparison theorems, we establish new results on asymptotic behavior of solutions of the studied equations. Obtained criteria improve and generalize earlier ones.