zbMATH — the first resource for mathematics

Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales. (English) Zbl 1075.39010
Authors’ abstract: We establish some sufficient conditions which guarantee that every solution of the third order nonlinear dynamic equation \((c(t)(a(t)x^\Delta (t))^\Delta )^\Delta +q(t)f(x(t))=0,\) \(t\geq t_0,\) oscillates or converges to zero.

39A12 Discrete version of topics in analysis
Full Text: DOI
[1] Agarwal, R.P.; Grace, S.R.; O’Regan, D., Oscillation theory for difference and functional differential equations, (2000), Kluwer Academic Publishers Dordrecht · Zbl 0969.34062
[2] R.P. Agarwal, S.R. Grace, D. O’Regan, Oscillation Theory for Second order Dynamic Equations, Series in Mathematical Analysis and Applications, 5, Taylor & Francis, London, 2003.
[3] Bohner, E.A.; Hoffacker, J., Oscillation properties of an Emden-Fowler type equation on discrete time scales, J. differential equations appl., 9, 603-612, (2003) · Zbl 1038.39009
[4] Bohner, M.; Došlý, O.; Kratz, W., An oscillation theorem for discrete eigenvalue problems, Rocky mountain J. math., 33, 4, 1233-1260, (2003) · Zbl 1060.39003
[5] Bohner, M.; Peterson, A., Dynamic equations on time scalesan introduction with applications, (2001), Birkhäuser Boston
[6] Bohner, M.; Saker, S.H., Oscillation of second order nonlinear dynamic equations on time scales, Rocky mountain J. math., 34, 4, 1239-1254, (2004) · Zbl 1075.34028
[7] M. Bohner, S.H. Saker, Oscillation criteria for perturbed nonlinear dynamic equations, submitted for publication. · Zbl 1112.34019
[8] O. Došlý, S. Hilger, A necessary and sufficient condition for oscillation of the Sturm-Liouville dynamic equation on time scales, in: R.P. Agarwal, M. Bohner, D. O’Regan (Eds.), special issue on Dynamic Equations on Time Scales, J. Comput. Appl. Math. 141 (2002) 147-158. · Zbl 1009.34033
[9] Erbe, L., Oscillation criteria for second order linear equations on a time scale, Canad. appl. math. quart., 9, 1-31, (2001) · Zbl 1050.39024
[10] Erbe, L.; Peterson, A., Positive solutions for a nonlinear differential equation on a measure chain, Math. comput. modelling, boundary value problems and related topics, 32, 571-585, (2000) · Zbl 0963.34020
[11] Erbe, L.; Peterson, A., Riccati equations on a measure chain, (), 193-199 · Zbl 1008.34006
[12] Erbe, L.; Peterson, A., Boundedness and oscillation for nonlinear dynamic equations on a time scale, Proc. amer. math. soc., 132, 735-744, (2004) · Zbl 1055.39007
[13] Erbe, L.; Peterson, A.; Rehak, P., Comparison theorems for linear dynamic equations on time scales, J. math. anal. appl., 275, 418-438, (2002) · Zbl 1034.34042
[14] Erbe, L.; Peterson, A.; Saker, S.H., Oscillation criteria for second-order nonlinear dynamic equations on time scales, J. London math. soc., 67, 701-714, (2003) · Zbl 1050.34042
[15] G.Sh. Guseinov, B. Kaymakçalan, On a disconjugacy criterion for second order dynamic equations on time scales, in: R.P. Agarwal, M. Bohner, D. O’Regan (Eds.), special issue on Dynamic Equations on Time Scales, J. Comput. Appl. Math. 141 (2002) 187-196. · Zbl 1014.34023
[16] Hilger, S., Analysis on measure chains—a unified approach to continuous and discrete calculus, Resultate math., 18, 18-56, (1990) · Zbl 0722.39001
[17] S. Huff, G. Olumolode, N. Pennington, A. Peterson, Oscillation of an Euler-Cauchy dynamic equation, Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, Wilmington, Discrete and Continuous Dynamical Systems, 2002, pp. 24-27. · Zbl 1052.39007
[18] Kamenev, I.V., An integral criterion for oscillation of linear differential equations of second order, Mat. zametki, 23, 249-251, (1978) · Zbl 0386.34032
[19] Saker, S.H., Oscillation of nonlinear dynamic equations on time scales, Appl. math. comput., 148, 81-91, (2004) · Zbl 1045.39012
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.