Some New Sufficient Conditions for The Oscillation of Nonlinear Ordinary Differential Equations


  • Jaffalah J . Amhalhil

الكلمات المفتاحية:

. Sufficient Conditions, Oscillation, Nonlinear Differential Equations.


In this research, we shall discuss the oscillation behavior of solutions for second order nonlinear differential equations. By employing a generalized Riccati transformation and an averaging technique, we derive some new oscillation conditions for all solutions. Our results are extention for some well known oscillation results. The relevance of our results is illustrated by some examples.



Agarwal, R. P. & Wang, QI-RU, 2004. Oscillation and Asymptotic Behavior for Second Order Nonlinear Perturbed Differential Equations. Math. And Comp. Modeling., 39: 1477-1490.

Amhalhil, J. J., 2021. Oscillations Of Solutions For Nonlinear Differential Equations. SUSJ, 11: 1-16.

Elabbasy, E. M., 2000. On the oscillation of nonlinear second order differential equations. Appl. Math. Comp. , 8: 76-83.

Elabbasy, E. M., & Elzeiny, Sh. R., 2011. Oscillation theorem concerning non-linear differential equations of the second order, Opu. Math. 31: 373-391.

Grace, S. R. & Lilli, B. S., 1990. Integral averaging techniques for the oscillation of second order nonlinear differential equations. J. Math. Anal. Appl. , 149: 227-311.

Graef, J. R. S., Rankin, M. & Spikes, P. W. 1978. Oscillation theorems for perturbed nonlinear differential equations, J. Math. Anal. Appl. , 65:375-390.

Li, W. T. & Cheng, S. S. 2002. An oscillation criteria for nonhomogeneous half- linear differential equations, Appl. Math. Lett. , 15: 256-263.

Manojlovic, J. V. 2001. Integral averaging and oscillation of second order nonlinear differential equations. Computers and Math. Applic. , 41: 1521-1534.

Salhin, A. A., 2019. Oscillation Theorems for Nonlinear Second Order Forced Differential Equations. SUSJ, 9: 125-138

Tiryaki, A. & Cakmak, D. 2004. Integral averaging and oscillation criteria of second order nonlinear differential equations. Cmputers and Math. Applic. , 47: 495-1506.