On the oscillation and asymptotic behavior of solutions of third order nonlineardifferential equations with mixed nonlinear neutral terms

Authors

SHAIMAA SALEMFollow
MOHAMED M. A. EL-SHEIKHFollow
AHMED MOHAMED HASSANFollow

Abstract

This paper is concerned with the oscillation and asymptotic behavior of solutions of third-order nonlinear neutral differential equations with a middle term and mixed nonlinear neutral terms in the case of the canonical operator. We establish several oscillation criteria that guarantee that all solutions are oscillatory or converge to zero. The given results are obtained by applying the comparison method, the Riccati transformation and the integral averaging technique. The results improve significantly and extend existing ones in the literature. Finally, illustrative examples are given.

DOI

10.55730/1300-0098.3503

Keywords

canonical operator, mixed neutral term, nonlinear neutral term, nonoscillation, Oscillation, third order differential equation

First Page

221

Last Page

247

Recommended Citation

SALEM, SHAIMAA; EL-SHEIKH, MOHAMED M. A.; and HASSAN, AHMED MOHAMED (2024) "On the oscillation and asymptotic behavior of solutions of third order nonlineardifferential equations with mixed nonlinear neutral terms," Turkish Journal of Mathematics: Vol. 48: No. 2, Article 9. https://doi.org/10.55730/1300-0098.3503
Available at: https://journals.tubitak.gov.tr/math/vol48/iss2/9