Third-Order Neutral Delay Differential Equations with Mixed Nonlinearities: Almost Oscillation via Linearization Method and Arithmetic-Geometric Inequality

In the present article, we create new sufficient conditions for the oscillatory and asymptotic behavior of solutions of the third-order nonlinear neutral delay differential equations with several super-linear and sub-linear terms. The results are obtained first by applying arithmetic-geometric mean inequality along with linearization method and then using comparison method as well as integral averaging technique. Finally, we show the importance and novelty of the main results by applying them to special cases of the studied equation.