Philos-Type Criteria for Testing the Oscillatory Performance of Solutions to Differential Equations With a Natural Argument - Amer, Ahmed E.; El-Owaidy, Hassan M.; El-Deeb, Ahmed A.; Moaaz, Osama (Communications in Mathematics and Applications, 2025)
The oscillatory performance of nonlinear delay differential equation solutions \((b ψ (u) [w']^r) '+q u^β (ρ) =0\) is examined in this work. The canonical case is considered, and Philos-type criteria are established to test the oscillation of all solutions. The existence of \(φ\) increases the difficulty in obtaining the asymptotic and monotonic properties of the solutions and also increases the possibility of applying the results to a broader range of special cases. The results obtained in this study represent an extension and generalization of earlier findings in the literature.