Abstract
Some Kamenev-type oscillation criteria are obtained for a second order quasilinear damped differential equation with impulses. These criteria generalize and improve some well-known results for second order differential equations with /and without impulses. In addition, new oscillation criteria are also obtained to generalize and improve known results. Two examples of applications are given to illustrate the theory.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chen, Y. S. and Feng, W. Z.,Oscillations of second order nonlinear ODE with impulses, J. Math. Anal. Appl.210 (1997), 150–169.
Hardy, G. H., Littlewood, J. E. and Polya, G.,Inequalities, 2nd Edition, Cambridge University Press, Cambridge, 1988.
Hsu, H. B. and Yeh, C. C.,Oscillation theorems for second order half-linear differential equations, Appl. Math. Lett.9 (1996), 71–77.
Kamenev, I. V.,An integral criterion for oscillation of linear differential equations of second order, Mat. Zametki.23 (1978), 249–251.
Lakshimikantham, V. and Bainov, D. D. and Simeonov, P. S.,Theory of Impulsive Differential Equations, Singapore, New Jersey, London: World Scientific Publishers, 1989.
Li, H. J. and Yeh, C. C.,An integral criteria for oscillation of nonlinear differential equations, Math.Japon.41 (1995), 185–188.
Li, H. J. and Yeh, C. C.,Oscillation criteria for nonlinear differential equations, Houston J. Math.21 (1995), 801–811.
Li, H. J. and Yeh, C. C.,Sturmain comparison theorem for half-linear second order differential equations, Proc. Roy. Soc. Edindburgh Sert. A125 (1995), 1193–1204.
Li, W. X., Yang, C. S. and Ji, H.,Oscillation of a class of second-order nonlinear ODE with impulses, Appl. Math. Comput.138 (2003), 181–188.
Luo, J. W. and Debnath, L.,Oscillations of second-order nonlinear ordinary differential equations with impulses, J. Math. Anal. Appl.240 (1999), 105–114.
Philos, Ch. G.,Oscillation theorems for linear differential equations of second order, Arch. Math (Basel).53 (1989), 482–492.
Takasi, K. and Yoshida, N.,Nonoscillation theorems for a class of quasilinear differential equations of second order, J. Math. Anal. Appl.189 (1995), 115–127.
Wong, P. J. Y. and Agarwal, R. P.,Oscillation criteria for half-linear differential equations, Adv. Math. Sci. Appl.9 (1999), 649–663.
Xu, Z. T. and Xia, Y.,Kamenev-type oscillation criteria for second-order quasilinear differential equations, Electronic J. Diff. Eq.2005(27) (2005), 1–9.
Yang, X. J.,Oscillation criteria for nonlinear differential equations with damping, Appl. Math. Comput.136 (2003), 549–557
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jin, C., Debnath, L. Oscillations of solutions of second order quasilinear differential equations with impulses. J. Appl. Math. Comput. 24, 1–16 (2007). https://doi.org/10.1007/BF02832297
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02832297