Abstract
The paper is concerned with the oscillation for a class of second-order nonlinear neutral perturbed dynamic equations on time scales. By employing the generalized Riccati transformation and introducing a general class of parameter functions, some new sufficient conditions for oscillation of such dynamic equations are established. Our results extend and improve some known results in the literature and the results in particular are essentially new under the weak conditions for the parameter functions. An example to illustrate the main results is given.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Hilger, S.: Analysis on measure chains–A unified approach to continuous and discrete calculus. Results Math. 18, 18–56 (1990)
Agarwal, R.P., Bohner, M., O’Regan, D., Peterson, A.: Dynamic equations on time scales, a survey. Comput. Appl. Math. 141, 1–26 (2002)
Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhauser, Boston (2001)
Hongyu, Y., Qi, G., Xiuping, Y.: Oscillation Criteria for Second Order Nonlinear Neutral Dynamic Equations on Time Scales. Mathematics in Practice and Theory. 18, 253–256 (2008)
Daxue, C., Jiachun, L.: Oscillation Theorems for Second-order Nonlinear Neutral Dynamic Equations on Time Scales. Sys. Sci. Math. Scis. 9, 1191–1205 (2010)
Agarwal, R.P., O’Regan, D., Saker, S.H.: Oscillation Criteria for Second-order Nonlinear Neutral Delay Dynamic Equations. Math. Anal. Appl. 300, 203–217 (2004)
Saker, S.H.: Oscillation of Second-order Nonlinear Neutral Delay Dynamic Equations on Time Scales. Math. Anal. Appl. 187, 123–141 (2006)
Sahiner, Y.: Oscillation of Second-order Neutral Delay and Mixed-type Dynamic Equations on Time Scales. Adv. Diff. Equ. 3, 1–9 (2006)
Jiashan, Y.: Oscillation for a Class of Second-order Nonlinear Dynamic Equations on Time Scales. Journal of Sichuan University (N.S.E.) 48, 278–283 (2011) (in Chinese)
Thandapani, E., Piramanantham, V.: Oscillation Criteria of Second Order Neutral Delay Dynamic Equations with Distributed deviating Arguments. Electronic J. of Qualitative Theory of Diff. Equ. 61, 1–15 (2010)
Petr, S., Bevan, T.: Applications of Maximum Principles to Dynamic Equations on Time scales. Diff. Equ. & Appl. 16, 373–388 (2010)
Anderson, D.: Oscillation and Nonoscillation Criteria for Two-Dimensional Time-Scale Systems of First-Order Nonlinear Dynamic Equations Electronic. J. of Diff. Equ. 24, 1–13 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yu, X., Sun, H., Yang, H., Jing, H. (2012). Oscillation Criteria for Nonlinear Neutral Perturbed Dynamic Equations on Time Scales. In: Liu, C., Wang, L., Yang, A. (eds) Information Computing and Applications. ICICA 2012. Communications in Computer and Information Science, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34041-3_43
Download citation
DOI: https://doi.org/10.1007/978-3-642-34041-3_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34040-6
Online ISBN: 978-3-642-34041-3
eBook Packages: Computer ScienceComputer Science (R0)