Abstract
We establish a new Kamenev-type theorem for a class of second-order nonlinear damped delay dynamic equations on a time scale by using the generalized Riccati transformation technique. The criterion obtained improves related contributions to the subject. An example is provided to illustrate assumptions in our theorem are less restrictive.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agarwal R P, Bohner M, Li T, et al. Hille and Nehari type criteria for third-order delay dynamic equations. J Difference Equ Appl, 2013, 19: 1563–1579
Agarwal R P, Bohner M, Saker S H. Oscillation of second order delay dynamic equations. Can Appl Math Q, 2005, 13: 1–17
Agarwal R P, Bohner M, Tang S, et al. Oscillation and asymptotic behavior of third-order nonlinear retarded dynamic equations. Appl Math Comput, 2012, 219: 3600–3609
Agarwal R P, O’Regan D, Saker S H. Oscillation criteria for second-order nonlinear neutral delay dynamic equations. J Math Anal Appl, 2004, 300: 203–217
Akın-Bohner E, Bohner M, Saker S H. Oscillation criteria for a certain class of second order Emden-Fowler dynamic equations. Electron Trans Numer Anal, 2007, 27: 1–12
Bohner M, Erbe L, Peterson A. Oscillation for nonlinear second order dynamic equations on a time scale. J Math Anal Appl, 2005, 301: 491–507
Bohner M, Peterson A. Dynamic Equations on Time Scales: An Introduction with Applications. Boston: Birkhäuser, 2001
Erbe L, Hassan T S, Peterson A. Oscillation criteria for nonlinear damped dynamic equations on time scales. Appl Math Comput, 2008, 203: 343–357
Erbe L, Peterson A, Saker S H. Oscillation criteria for second-order nonlinear delay dynamic equations. J Math Anal Appl, 2007, 333: 505–522
Grace S R, Bohner M, Agarwal R P. On the oscillation of second-order half-linear dynamic equations. J Difference Equ Appl, 2009, 15: 451–460
Hassan T S. Kamenev-type oscillation criteria for second order nonlinear dynamic equations on time scales. Appl Math Comput, 2011, 217: 5285–5297
Hassan T S, Erbe L, Peterson A. Oscillation of second order superlinear dynamic equations with damping on time scales. Comput Math Appl, 2010, 59: 550–558
Hassan T S, Erbe L, Peterson A. Oscillation criteria for second order sublinear dynamic equations with damping term. J Difference Equ Appl, 2011, 17: 505–523
Karpuz B. Li type oscillation theorem for delay dynamic equations. Math Methods Appl Sci, 2013, 36: 993–1002
Karpuz B, Öcalan Ö. Necessary and sufficient conditions on asymptotic behaviour of solutions of forced neutral delay dynamic equations. Nonlinear Anal TMA, 2009, 71: 3063–3071
Li T, Saker S H. A note on oscillation criteria for second-order neutral dynamic equations on isolated time scales. Commun Nonlinear Sci Numer Simul, 2014, 19: 4185–4188
Saker S H. Oscillation Theory of Dynamic Equations on Time Scales, Second and Third Orders. Berlin: Lambert Academic Publishing, 2010
Saker S H, Agarwal R P, O’Regan D. Oscillation of second-order damped dynamic equations on time scales. J Math Anal Appl, 2007, 330: 1317–1337
Şahiner Y. Oscillation of second-order delay differential equations on time scales. Nonlinear Anal TMA, 2005, 63: 1073–1080
Şenel M T. Kamenev-type oscillation criteria for the second-order nonlinear dynamic equations with damping on time scales. Abstr Appl Anal, 2012, 2012: 1–18
Zhang C, Li T, Agarwal R P, et al. Oscillation results for fourth-order nonlinear dynamic equations. Appl Math Lett, 2012, 25: 2058–2065
Zhang Q. Oscillation of second-order half-linear delay dynamic equations with damping on time scales. J Comput Appl Math, 2011, 235: 1180–1188
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bohner, M., Li, T. Kamenev-type criteria for nonlinear damped dynamic equations. Sci. China Math. 58, 1445–1452 (2015). https://doi.org/10.1007/s11425-015-4974-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11425-015-4974-8