Fourth-Order Differential Equations: Asymptotic andOscillatory Behaviors of Solutions (European Journal of Pure and Applied Mathematics, 2025)
Our aim in this work is to derive conditions and criteria for the oscillation of some differential equations of p-Laplace type with a delayed term. Therefore, we develop these criteria that confirm to us that the equations studied are oscillatory by applying comparison with lower-order equations and Riccati techniques . Finally, we can elucidate the meaning of the new inequalitiesby applying our findings to a few particular cases of the studied equation. Our findings build on earlier findings that looked at equations with a delay term and operators of the p-Laplace type. To demonstrate the importance of the acquired results, we provide an example.
Keywords: Asymptotic behavior, p-Laplacian, fourth-order, delay di§erential equations