On the oscillation and non-oscillation of solutions of forced second order differential equations
Volume 30, Issue 2, pp 101--115
https://doi.org/10.22436/jmcs.030.02.02
Publication Date: December 02, 2022
Submission Date: August 11, 2022
Revision Date: October 06, 2022
Accteptance Date: November 10, 2022
Authors
S. E. Tallah
- Department of Mathematics, University College for Women, Ain shams University, Cairo, Egypt.
M. M. A. El-sheikh
- Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom, Egypt.
G. A. F. Ismail
- Department of Mathematics, University College for Women, Ain shams University, Cairo, Egypt.
Abstract
The oscillatory behavior of solutions of a class of second order forced
non-linear differential equations is discussed. Several oscillation and
non-oscillation criteria are established using Riccati transformations
technique. Four examples are given to illustrate our results.
Share and Cite
ISRP Style
S. E. Tallah, M. M. A. El-sheikh, G. A. F. Ismail, On the oscillation and non-oscillation of solutions of forced second order differential equations, Journal of Mathematics and Computer Science, 30 (2023), no. 2, 101--115
AMA Style
Tallah S. E., El-sheikh M. M. A., Ismail G. A. F., On the oscillation and non-oscillation of solutions of forced second order differential equations. J Math Comput SCI-JM. (2023); 30(2):101--115
Chicago/Turabian Style
Tallah, S. E., El-sheikh, M. M. A., Ismail, G. A. F.. "On the oscillation and non-oscillation of solutions of forced second order differential equations." Journal of Mathematics and Computer Science, 30, no. 2 (2023): 101--115
Keywords
- Differential equations
- interval oscillation
- forcing terms
- damped equations
MSC
References
-
[1]
H. K. Abdullah, A note on the oscillation of the second order differential equations, Czech. Math. J., 54 (2004), 949–954
-
[2]
D. Cakmak, Oscillation for second order nonlinear differential equations with damping, Dyn. Sys. Appl., 17 (2008), 139–148
-
[3]
M. M. A. El-Sheikh, Oscillation and nonoscillation criteria for second order nonlinear differential equations. I, J. Math. Anal. Appl., 179 (1993), 14–27
-
[4]
S. R. Grace, Oscillation theorems for second order nonlinear differential equations with damping, Math. Nachr., 141 (1989), 117–127
-
[5]
S. R. Grace, Oscillation criteria for second order nonlinear differential equations with damping, J. Austral. Math. Soc. Ser. A, 49 (1990), 43–54
-
[6]
Y. Huang, F. Meng, oscillation criteria for forced second-order nonlinear differential equations with damping, J. Comput. Appl. Math., 224 (2009), 339–345
-
[7]
F. Jiang, F. Meng, New oscillation criteria for a class of second order nonlinear forced differential equations, J. Math. Anal. Appl., 336 (2007), 1476–1485
-
[8]
H. J. Li, Oscillation criteria for second order linear differential equation, J. Math. Anal. Appl., 194 (1995), 217–234
-
[9]
W.-T. Li, Interval oscillation criteria for second order nonlinear differential equations with damping, Taiwanese J. Math., 7 (2003), 461–475
-
[10]
W.-T. Li, H.-F. Huo, Interval oscillation criteria for nonlinear second order differential equations, Indian J. Pure Appl. Math., 32 (2001), 1003–1014
-
[11]
T. Li, Y. V. Rogovchenko, S. Tang, Oscillation of second order nonlinear differential equations with damping, Math. Slovaca, 64 (2014), 1227–1236
-
[12]
O. G. Mustafa, S. P. Rogovchenko, Y. V. Rogovchenko, Oscillation of nonliner second order equations with damping term, J. Math. Anal. Appl., 298 (2004), 604–620
-
[13]
S. ¨O ˘grekc¸i, A. Misir, A. Tiryaki, On the oscillation of second order nonlinear differential equations with damping, Miskolc Math. Notes, 18 (2017), 365–378
-
[14]
Ch. G. Philos, On a Kamenev’s integral criterion for oscillation of linear differential equations of second order, Utilitas Math., 24 (1983), 277–289
-
[15]
Y. V. Rogovchenko, Oscillation theorems for second order equations with damping, Nonlinear Anal., 41 (2000), 1005– 1028
-
[16]
S. P. Rogovchenko, Yu. V. Rogovchenko, Oscillation of differential equations with damping, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 10 (2003), 447–461
-
[17]
Y. V. Rogovchenko, F. Tuncay, Interval oscillation criteria for second order nonlinear differential equations with damping, Dynam. Systems Appl., 16 (2007), 337–343
-
[18]
Y. V. Rogovchenko, F. Tuncay, Oscillation theorems for a class of second order nonlinear differential equations with damping, Taiwanese J. Math., 13 (2009), 1909–1928
-
[19]
W. Shi, Interval oscillation criteria for a forced second-order differential equation with nonlinear damping, Math. Comput. Modelling, 43 (2006), 170–177
-
[20]
I. M. Sobol, Investigation with the aid of polar coordinates of the asymptotic behavior of solutions of a linear differential equation of the second order, Math. Sb., 28 (1951), 707–714
-
[21]
A. Tiryakia, A. Zafer, Interval oscillation of a general class of second-order nonlinear differential equations with nonlinear damping, Nonlinear Anal., 60 (2005), 49-–63
-
[22]
E. Tunc, Interval oscillation criteria for certain forced second-order differential equations, Carpathian J. Math., 28 (2012), 337—344
-
[23]
E. Tunc¸, H. Avci, Interval oscillation criteria for second order nonlinear differential equations with nonlinear damping, Miskolc Math. Notes, 14 (2013), 307–321
-
[24]
E. Tunc¸, A. Kaymaz, New oscillation results for forced second order differential equations with mixed nonlinearities, Appl. Math., 3 (2012), 147–153
-
[25]
J. S. W. Wong, On Kamenev-type oscillation for second order differential equations with damping, J. Math. Anal. Appl., 248 (2001), 244–257
-
[26]
J. R. Yan, On some properties of solutions of second order nonlinear differential equations, J. Math. Anal. Appl., 138 (1989), 75–83
-
[27]
X. Yang, Oscillation criteria for nonlinear differential equations with damping, Appl. Math. Comput., 136 (2003), 549– 557
-
[28]
Q. Zhang, X. Song, S. Liu, New oscillation criteria for the second order nonlinear differential equations with damping, J. Appl. Math. Phys., 4 (2016), 1179–1185