# Kamenev type oscillation criteria for second order impulsive differential equations

Volume 26, Issue 2, pp 172--183
Publication Date: November 05, 2021 Submission Date: June 24, 2021 Revision Date: August 17, 2021 Accteptance Date: September 17, 2021
• 409 Views

### Authors

S. E. Tallah - Department of Mathematics, University College for women, Ain shams university, Cairo, Egypt. M. M. A. Elsheikh - 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 oscillation of second order impulsive differential equations is discussed using Riccati transformations technique. New oscillation criteria are established, to improve and extend some recent results in the literature. Two illustrative examples are given.

### Share and Cite

##### ISRP Style

S. E. Tallah, M. M. A. Elsheikh, G. A. F. Ismail, Kamenev type oscillation criteria for second order impulsive differential equations, Journal of Mathematics and Computer Science, 26 (2022), no. 2, 172--183

##### AMA Style

Tallah S. E., Elsheikh M. M. A., Ismail G. A. F., Kamenev type oscillation criteria for second order impulsive differential equations. J Math Comput SCI-JM. (2022); 26(2):172--183

##### Chicago/Turabian Style

Tallah, S. E., Elsheikh, M. M. A., Ismail, G. A. F.. "Kamenev type oscillation criteria for second order impulsive differential equations." Journal of Mathematics and Computer Science, 26, no. 2 (2022): 172--183

### Keywords

• Kameneve type oscillation
• damping terms
• impulsive
• Riccati transformations

•  34A37
•  34C10
•  34C29

### References

• [1] U. A. Abasiekwere, I. M. Esuabana, I. O. Isaac, Z. Lipscey, Oscillations of second order impulsive differential equations with advanced arguments, Global J. Sci. Frontier Res. Math. Decis. Sci. (USA), 18 (2018), 25--32

• [2] H. K. Abdullah, A note on the oscillation of the second order differential equations, Czechoslovak Math. J., 54 (2004), 949--954

• [3] R. P. Agarwal, M. Bohner, T. X. Li, Oscillatory behavior of second-order half-linear damped dynamic equations, Appl. Math. Comput., 254 (2015), 408--418

• [4] R. P. Agarwal, M. Bohner, T. X. Li, C. H. Zhang, Oscillation criteria for second-order dynamic equations on time scales, Appl. Math. Lett., 31 (2014), 34--40

• [5] R. P. Agarwal, F. Karakoç, A survey on oscillation of impulsive delay differential equations, Comput. Math. Appl., 60 (2010), 1648–1685

• [6] R. P. Agarwal, F. Karakoç, A. Zafer, A survey on oscillation of impulsive differential equations, Adv. Difference Equ., 2010 (2010), 52 pages

• [7] R. P. Agarwal, C. H. Zhang, T. X. Li, New Kamenev-type oscillation criteria for second-order nonlinear advanced dynamic equations, Appl. Math. Comput., 225 (2013), 822--828

• [8] D. D. Bainov, P. Simeonov, Oscillation theory of impulsive differential equations, International Publications, Orlando (1998)

• [9] M. Bohner, T. S. Hassan, T. X. Li, Fite-Hille-Wintner-type oscillation criteria for second-order half-linear dynamic equation with deviating arguments, Indag. Math. (N.S.), 29 (2018), 548--560

• [10] M. Bohner, T. X. Li, Kamenev-type criteria for nonlinear damped dynamic equations, Sci. China Math., 58 (2015), 1445--1452

• [11] J. Džurina, S. R. Grace, I. Jadlovska, T. X. Li, Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr., 293 (2020), 910--922

• [12] I. M. Esuabana, U. A. Abasiekwere, On stability of first order linear impulsive differential equations, Int. J. Stat. Appl. Math., 3 (2018), 231--236

• [13] Z. M. He, W. G. Ge, Oscillation of second order nonlinear impulsive ordinary differential equations, J. Comput. Appl. Math., 158 (2003), 397--406

• [14] V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific Publishing Co., Teaneck (1989)

• [15] J. H. Li, Oscillation criteria for second order linear differential equations, J. Math. Anal. Appl., 194 (1995), 217--234

• [16] T. X. Li, N. Pintus, G. Viglialoro, Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys., 70 (2019), 18 pages

• [17] T. X. Li, Y. V. Rogovchenko, Oscillation criteria for second--order superlinear Emden--Fowler neutral differential equations, Monatsh. Math., 184 (2017), 489--500

• [18] T. X. Li, Y. V. Rogovchenko, S. H. Tang, Oscillation of second-order nonlinear differential equations with damping, Math. Slovaca, 64 (2014), 1227--1236

• [19] T. X. Li, S. H. Saker, A note on oscillation criteria for second-order neutral dynamic equations on isolated time scales, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 4185--4188

• [20] T. Li, G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even in the attraction dominated regime, Differ. Integ. Equ., 34 (2021), 315--336

• [21] Y. V. Rogovchenko, Oscillation theorems for second order equations with damping, Nonlinear Anal., 41 (2000), 1005--1028

• [22] J. Sugie, Interval criteria for oscillation of second order self-adjoint impulsive differential equations, Proc. Amer. Math. Soc., 148 (2019), 1095--1108

• [23] J. Sugie, K. Ishihara, Philos-type oscillation criteria for linear differential equations with impulsive effects, J. Math. Anal. Appl., 470 (2019), 911--930

• [24] G. Viglialoro, On the blow-up time of a parabolic system with damping terms, C. R. Acad. Bulgare Sci., 67 (2014), 1223--1232

• [25] K. W. Wen, Y. P. Zeng , H. Q. Peng, L. F. Huang, Philos-type oscillation criteria for second-order linear impulsive differential equation with damping, Bound. Value Probl., 111 (2019), 16 pages

• [26] D. Willett, On the oscillatory behavior of the solutions of second order differential equations, Ann. Polon Math., 21 (1969), 175--194

• [27] J. R. Yan, A note on an oscillation criterion for an equation with damped term, Proc. Amer. Math. Soc., 90 (1984), 277--280

• [28] C. H. Zhang, R. P. Agarwal, T. X. Li, Oscillation and asymptotic behavior of higher-order delay differential equations with $p$-Laplacian like operators, J. Math. Anal. Appl., 409 (2014), 1093--1106