Second-Order Noncanonical Delay Differential Equations with Sublinear and Superlinear Terms: New Oscillation Criteria via Canonical Transform and Arithmetic–Geometric Inequality

Abstract

In this paper, the authors present new oscillation criteria for the noncanonical second-order delay differential equation with mixed nonlinearities

$$\begin{aligned} (a(t)x^{\prime }(t))^{\prime }+ \sum _{j=1}^{n} q_{j}(t) x^{\alpha _{j}}(\sigma _{j}(t))=0 \end{aligned}$$

using an arithmetic–geometric mean inequality. We establish our results first by transforming the studied equation into canonical form and then applying a comparison technique and integral averaging method to get new oscillation criteria. Examples are provided to illustrate the importance and novelty of their main results.