Oscillation of Superlinear second Order Nonlinear Differential Equations with Damping Term
DOI:
https://doi.org/10.37375/sjfssu.v3i2.1476Keywords:
Oscillation, super-linear, second order, nonlinear differential equations, damping term.Abstract
The study of differential equations has been the object of many researchers over the last decades. Different approaches and various techniques have been adopted to investigate the qualitative properties of their solutions. Recently and driven by their widespread applications, the investigation of differential equations of second order has drawn significant attention. The oscillation of solutions has been the main features that have attracted consideration. Therefore, it has been intended to use the Riccati Transformation Technique for obtaining several new oscillation criteria for different classes of nonlinear differential equations of the second order with a damping term. Oscillatory behavior has taken into account through this study of solutions of some differential equations. Comparisons between our results and the previously known results have presented. The relevance of our theorems has been clear clear due to carefully selected examples. As a conclusion, our aim is to provide some results to improve and/or extend some of well-known results in the literature.
References
Atkinson, F. V. (1955). On second order nonlinear oscillations. Pacific. J. Math.,) 5), 643-647.
Ayanlar, B. and Tiryaki, A. (2000). Oscillation theorems for nonlinear second order differential equations with damping. Acta Math. Hungar., (89), 1-13.
Beqiri, X. and Koci, E. (2014). New Oscillation and Non-oscillation Criteria for Second Order Nonlinear Differential Equations. Int. J. of Pur. and Appl. Math.,93(2), 155-163.
Bhatia, N. P. (1966). Some oscillation theorems for second order differential equations. J. Math. Anal. Appl., (15), 442-446.
Bihari, I. (1963). An oscillation theorem concerning the half linear differential equation of the second order. Magyar Tud. Akad. Mat. Kutato Int.Kozl., (8), 275-280.
Berkane, A. (2008). Sufficient conditions for the oscillation of solutions to nonlinear second order differential equations. Electronic J. of Differential Equations, (3), 1-6.
Elabbasy, E. M. and Elzeine, S. R. (2011). Oscillation theorems concerning nonlinear differential equations of the second order, Opuscula Math., (31), 373-391.
Lee, Chung-Fen and Yeh, Chen-Chin (2007). An oscillation theorem, Applied Mathematics Letters, (20), 238-240.
El-abbasy, E. M. Hassan, Taher S. and Saker, Samir H. (2005). Oscillation of second- order non-linear differential equations with a damping term. Electronic Journal of differential equations vol., (76), 1-13.
Elabbasy, E. M. and Elhaddad, W. W. (2007). Oscillation of second order non-linear differential equations with a damping term. Electronic Journal of Qualitative Theory of Differential Equations, (25), 1-19.
Fite, W. B. (1918). Concerning the zeros of the solutions of certain differential equations. Trans. Amer. Math. Soc., (19), 341-352.
Grace, S. R. and Lalli, B. (1980). Oscillation theorems second perturbed differential equations. J. Math. Anal. Appl., (77), 205-214.
Greaf, J. R. Rankin, S. M. and Spikes, P. W. (1978). Oscillation theorems for perturbed nonlinear differential equations. J. Math. Anal. Appl. (65), 375-390.
Kamenev, I. V. (1978). Integral criterion for oscillation of linear differential equations of second order. Math. Zametki (23), 249-251.
Kartsatos, A. G. (1968). On oscillations of nonlinear equations of second order. J. Math. Anal. Appl., (24), 665-668.
Kirane, M. and Rogovchenko, Y. V. (2000). Oscillation results for second order damped differential equations with nonmonotonous nonlinearity. J. Math. Anal. Appl. (250), 118-138.
Kirane, M. and Rogovchenko, Y. V. (2001). On oscillation of nonlinear second order differential equation with damping term. Appl. Math. and Comput., (117), 177-192.
Lu, F. and Meng, F. (2007). Oscillation theorems for superlinear second order nonlinear damped differential equations. Appl. Math. and Comput., (189), 796-804.
Remili, M. (2008). Oscillation theorem for perturbed nonlinear differential equations. Int. Math. Forum., (11) 513-524.
Mustafa, O. G. Rogovchenko, S. P. and Rogovchenko, Y. V. (2004). On oscillation of nonlinear second order differential equations with damping term. J. Math. Anal. Appl. (298), 604-620.
Nagabuchi, Y. and Yamamoto, M. (1988). Some oscillation criteria for second order nonlinear ordinary differential equations with damping. Proc. Japan. Acad., (64), 282-285.
Naito, M. (1974). Oscillation criteria for a second order differential equation with a damping term. Hiroshima Math. J. (4), 285-291.
Manojlovic, J. V. (2001). Integral averages and oscillation of second order nonlinear differential equations. Computers and Math. Applic., (41),1521-1534.
Remili, M. (2010). Oscillation criteria for second order nonlinear perturbed differential equations. Electronic Journal of Qualitative Theory of Differential Equations, (25), 1-11.
Rogovchenko, S. P. and Rogovchenko, Y. V. (2003). Oscillation of differential equations with damping. Dyn. Contin. Discrete Impuls. Sys. Ser. A Math. Anal., (10), 447-461.
Rogovchenko, Y. V. and Tuncay, F. (2007). Interval oscillation of a second order nonlinear differential equation with a damping term. Discrete and Continuous Dynamical Systems Supplement, 883-891.
Rogovchenko, Y. V. and Tuncay, F. (2008). Oscillation criteria for second order nonlinear equations with damping. Nonlinear Analysis, (69), 208-221.
Rogovchenko, Y. V. and Tuncay, F. (2009). Oscillation theorems for a class of second order Nonlinear differential equations with damping. Taiwanese J. of Math., (13), 1909-1928.
Saker, H. S. Pang, P. Y. H. and Agrawal, R. P. (2003). Oscillation theorems for second order nonlinear functional differential equations with damping. Dynamic Sys. Appl., (12), 307-322.
Temtek, P. and Tiryaki, A. (2013). Oscillation criteria for a certain second order nonlinear perturbed differential equations. J. of Inequalities and Appl., 524 1-12.
Tunc, E. and Avci, H. (2012). Oscillation criteria for a class of second order nonlinear differential equations with damping. Bull. of Math. Anal. and Appl., 4(2) 40-50.
Wang, X. J. and Song, G. H. (2011). Oscillation criteria for a second order nonlinear damped differential equation. Inter. J. of Info. and Syst. Scie., 7 73-82.
Wang, X.J. and Song, G. H. (2013). Oscillation theorems for a class of nonlinear second order differentia;l equations with damping. Advances in Pure Mathematics, (3) 226-233.
Xiaoling, F. L. and Chenghui, Z. (2013). Oscillation of second-order dampeddifferential equations. Advances in Difference Equations., 326 1-11.
Xhevair, B. and Elisabeta, K. (2014). New Oscillation and Non-oscillation Criteria for Secnd Order Nonlinear Differential Equations. International Journal of Pure and Applied Mathematics., 93 (2), 155-163.
Zhang, M. and Song, G. H. (2011) Oscillation theorems for second order nonlinear perturbed differential equations with damping. J. Shanghai Univ. (Engl. Ed.) 15(6) 510-516.
Zheng, Z. (2006). Oscillation criteria for nonlinear second order differential equations with damping. Acta Math. Hungarica, (110), 241-252.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Scientific Journal for Faculty of Science-Sirte University
This work is licensed under a Creative Commons Attribution 4.0 International License.
