Research ArticleOpen AccessGoogle Scholar indexed
New Oscillation Criteria of Second-Order Nonlinear Delay Dynamic Equations on Time Scales
Department of Mathematics, Binzhou University, Shandong, China
Department of Mathematics, Binzhou University, Shandong, China
- 1 Department of Mathematics, Binzhou University, Shandong, China
- 2 Department of Mathematics, Binzhou University, Shandong, China
Applied Mathematics·Volume 05 (2014)·Pages 3474–3483·Published 1 December 2014·DOI10.4236/am.2014.521325
Copy link · social · email
Abstract
By using the generalized Riccati transformation and the integral averaging technique, the paper establishes some new oscillation criteria for the second-order nonlinear delay dynamic equations on time scales. The results in this paper unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. The Theorems in this paper are new even in the continuous and the discrete cases.
KeywordsOscillation CriterionDynamic EquationsTime Scale
- Agarwal, R.P., Bohner, M. and Saker, S.H. (2005) Oscillation of Second Order Delay Dynamic Equations. Quarterly of Applied Mathematics, 13, 1-18.
- Sahiner. Y. (2005) Oscillation of Second Order Delay Differential Equations on Time Scales. Nonlinear Analysis: Theory, Methods & Applications, 63, 1073-1080. http://dx.doi.org/10.1016/j.na.2005.01.062
- Erbe, L., Peterson, A. and Saker, S.H. (2007) Oscillation Criteria for Second Order Nonlinear Delay Dynamic Equations. Journal of Mathematical Analysis and Applications, 333, 505-522. http://dx.doi.org/10.1016/j.jmaa.2006.10.055
- Saker, S.H. (2005) Oscillation Criteria of Second-Order Half-Linear Dynamic Equations on Time Scales. Journal of Computational and Applied Mathematics, 177, 375-387. http://dx.doi.org/10.1016/j.cam.2004.09.028
- Grace, S.R., Bohner, M. and Agarwal, R.P. (2009) On the Oscillation of Second-Order Half-Linear Dynamic Equations. Journal of Difference Equations and Applications, 15, 451-460. http://dx.doi.org/10.1080/10236190802125371
- Bohner, M. and Saker, S.H. (2004) Oscillation of Second Order Nonlinear Dynamic Equations on Time Scales. Rocky Mountain Journal of Mathematics, 34, 1239-1245. http://dx.doi.org/10.1216/rmjm/1181069797
- Erbe, L. (2001) Oscillation Criteria for Second Order Linear Equations on a Time Scale. The Canadian Applied Mathematics Quarterly, 9, 345-375.
- Zhang, Q., Song, X. and Gao, L. (2012) On the Oscillation of Second-Order Nonlinear Delay Dynamic Equations on Time Scales. Applied Mathematics & Information Sciences, 30, 219-234.
- Zhang, Q., Gao, L. and Wang, L. (2011) Oscillation of Second-Order Nonlinear Delay Dynamic Equations on Time Scales. Computers & Mathematics with Applications, 61, 2342-2348. http://dx.doi.org/10.1016/j.camwa.2010.10.005
- Han, Z., Li, T., Sun, S. and Zhang, C. (2009) Oscillation for Second-Order Nonlinear Delay Dynamic Equations on Time Scales. Advances in Difference Equations, Article ID: 756171, 13 pages.
- Bohner, M. and Peterson, A. (2001) Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston. http://dx.doi.org/10.1007/978-1-4612-0201-1
- Bohner, M. and Peterson, A. (2003) Advances in Dynamic Equations on Time Scales. Birkh?user, Boston. http://dx.doi.org/10.1007/978-0-8176-8230-9
- Sun, S., Han, Z. and Zhang, C. (2009) Oscillation of Second Order Delay Dynamic Equations on Time Scales. Journal of Applied Mathematics and Computing, 30, 459-468. http://dx.doi.org/10.1007/s12190-008-0185-6