×
Agarwal, Ravi P.; O’Regan, Donal; Saker, S. H.

Oscillation criteria for nonlinear perturbed dynamic equations of second-order on time scales. (English) Zbl 1089.39001

J. Appl. Math. Comput. 20, No. 1-2, 133-147 (2006).
This paper deals with the oscillatory behavior of second-order nonlinear perturbed dynamic equations on time scales by means of the well-known Riccati transformation technique. An example which illustrates the importance of the main results is also included.
Reviewer: Mingshu Peng (Beijing)

Cited in 10 Documents

MSC:

39A11 Stability of difference equations (MSC2000)
34K11 Oscillation theory of functional-differential equations
39A12 Discrete version of topics in analysis

Keywords:

oscillation; second-order nonlinear dynamic equation; time scale; Riccati transformation technique
PDF BibTeX XML Cite
\textit{R. P. Agarwal} et al., J. Appl. Math. Comput. 20, No. 1--2, 133--147 (2006; Zbl 1089.39001)
Full Text: DOI

References:

[1] R. P. Agarwal, M. Bohner, D. O’Regan and A. Peterson,Dynamic equations on time scales: A survey, Special Issue on ”Dynamic Equations on Time Scales”, edited by R. P. Agarwal, M. Bohner, and D. O’Regan, (Preprint in Ulmer Seminare 5) J. Comp. Appl. Math.141 (2002), 1–26. · Zbl 1020.39008
[2] R. P. Agarwal, M. Bohner and S. H. Saker,Oscillation of second order delay dynamic equations, Canadian Appl. Math. Quart. (accepted). · Zbl 1126.39003
[3] R. P. Agarwal, D. O’Regan and S. H. Saker,Oscillation criteria for second-order nonlinear neutral delay dynamic equations, J. Math. Anal. Appl.300 (2004), 203–217. · Zbl 1062.34068
[4] R. P. Agarwal, D. O’Regan and S. H. Saker,Philos-type oscillation criteria of second-order half-linear dynamic equations on time scales, submitted. · Zbl 1139.34029
[5] R. P. Agarwal, D. O’Regan and S. H. Saker,Properties of bounded solutions of nonlinear dynamic equations on time scales, submitted.
[6] E. A. Bohner and J. Hoffacker,Oscillation properties of an Emden-Fowler type Equations on Discrete time scales, J. Diff. Eqns. Appl.9 (2003), 603–612. · Zbl 1038.39009
[7] M. Bohner and A. Peterson,Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001. · Zbl 0978.39001
[8] M. Bohner, A. Peterson,Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003. · Zbl 1025.34001
[9] M. Bohner and S. H. Saker,Oscillation of second order nonlinear dynamic equations on time scales, Rocky Mountain J. Math.34 (2004), 1239–1254. · Zbl 1075.34028
[10] M. Bohner and S. H. Saker,Oscillation criteria for perturbed nonlinear dynamic equations, Math. Comp. Modelling40 (2004), 249–260. · Zbl 1112.34019
[11] E. A. Bohner, M. Bohner and S. H. Saker,Oscillation criteria for a certain class of second order Emden-Fowler dynamic Equations, Elect. Transc. Numerical. Anal. (accepted). · Zbl 1177.34047
[12] O. Doslý and S. Hilger,A necessary and sufficient condition for oscillation of the Sturm-Liouville dynamic equation on time scales, Special Issue on ”Dynamic Equations on Time Scales”, edited by R. P. Agarwal, M. Bohner, and D. O’Regan, J. Comp. Appl. Math.141 (2002) 147–158. · Zbl 1009.34033
[13] L. Erbe,Oscillation criteria for second order linear equations on a time scale, Canadian Appl. Math. Quart.9 (2001), 1–31. · Zbl 1050.39024
[14] L. Erbe and A. Peterson,Positive solutions for a nonlinear differential equation on a measure chain, Mathl. Comp. Modelling, Boundary Value Problems and Related Topics32(5-6), (2000), 571–585. · Zbl 0963.34020
[15] L. Erbe and A. Peterson,Riccati equations on a measure chain, In G. S. Ladde, N. G. Medhin, and M. Sambandham, editors, Proceedings of Dynamic Systems and Applications 3, 193–199, Atlanta, 2001, Dynamic Publishers. · Zbl 1008.34006
[16] L. Erbe and A. Peterson,Oscillation criteria for second order matrix dynamic equations on a time scale, Special Issue on ”Dynamic Equations on Time Scales”, edited by R. P. Agarwal, M. Bohner, and D. O’Regan, J. Comput. Appl. Math.141 (2002), 169–185. · Zbl 1017.34030
[17] L. Erbe and A. Peterson,Boundedness and oscillation for nonlinear dynamic equations on a time scale, Proc. Amer. Math. Soc.132 (2004), 735–744. · Zbl 1055.39007
[18] L. Erbe, A. Peterson and S. H. Saker,Oscillation criteria for second-order nonlinear dynamic equations on time scales, J. London Math. Soc.67 (2003), 701–714. · Zbl 1050.34042
[19] G. H. Hardy, J. E. Littlewood and G. Polya,Inequalities, 2nd Ed. Cambridge Univ. Press 1952.
[20] S. Hilger,Analysis on measure chains –a unified approach to continuous and discrete calculus, Results Math.18 (1990), 18–56. · Zbl 0722.39001
[21] S. H. Saker,Oscillation of nonlinear dynamic equations on time scales, Appl. Math. Comp.148 (2004), 81–91. · Zbl 1045.39012
[22] S. H. Saker,Oscillation criteria of second-order half-linear dynamic equations on time scales, J. Comp. Appl. Math.177 (2005), 375–387. · Zbl 1082.34032
[23] S. H. Saker,Boundedness of solutions of second-order forced nonlinear dynamic equations, Rocky Mount. J. Math (accepted). · Zbl 1139.34030
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.