×
Grace, Said R.; Agarwal, Ravi P.; Bohner, Martin; O’Regan, Donal

Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations. (English) Zbl 1221.34083

Commun. Nonlinear Sci. Numer. Simul. 14, No. 8, 3463-3471 (2009).
Summary: We establish some new criteria for the oscillation of second-order nonlinear dynamic equations on a time scale. We study the case of strongly superlinear and the case of strongly sublinear equations subject to various conditions.

Cited in 49 Documents

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34N05 Dynamic equations on time scales or measure chains

Keywords:

dynamic equation; time scale; nonlinear; superlinear; sublinear; oscillation
PDF BibTeX XML Cite
\textit{S. R. Grace} et al., Commun. Nonlinear Sci. Numer. Simul. 14, No. 8, 3463--3471 (2009; Zbl 1221.34083)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Agarwal, R.; Bohner, M.; Li, W.-T., Nonoscillation and oscillation theory for functional differential equations, Monographs and textbooks in pure and applied mathematics, (2004), Marcel Dekker New York
[2] Agarwal, R.P.; Bohner, M.; Grace, S.R., On the oscillation of second-order half-linear dynamic equations, J differ equ appl, (2008), (to appear)
[3] Agarwal, R.P.; Bohner, M.; Grace, S.R., Oscillation criteria for first-order forced nonlinear dynamic equations, Can appl math Q, 15, 3, (2008), (to appear)
[4] Agarwal, R.P.; Bohner, M.; Grace, S.R.; O’Regan, D., Discrete oscillation theory, (2005), Hindawi Publishing New York · Zbl 1084.39001
[5] Agarwal RP, Bohner M, O’Regan D, Peterson A. Dynamic equations on time scales: a survey. J Comput Appl Math 2002;141(1-2):1-26. Agarwal RP, Bohner M, O’Regan D, editors. Special issue on dynamic equations on time scales. Preprint in Ulmer Seminare 5. · Zbl 1020.39008
[6] Agarwal, R.P.; Grace, S.R.; O’Regan, D., Oscillation theory for difference and functional differential equations, (2000), Kluwer Academic Publishers Dordrecht · Zbl 0954.34002
[7] Agarwal, R.P.; Grace, S.R.; O’Regan, D., Oscillation theory for second order linear, half-linear, superlinear and sublinear dynamic equations, (2002), Kluwer Academic Publishers Dordrecht · Zbl 1073.34002
[8] Agarwal RP, Grace SR, O’Regan D. On the oscillation of certain second order difference equations. J Differ Equ Appl 2003;9(1):109-119. In honour of Professor Allan Peterson on the occasion of his 60th birthday, Part II.
[9] Agarwal, R.P.; Grace, S.R.; O’Regan, D., Oscillation theory for second order dynamic equations, Series in mathematical analysis and applications, vol. 5, (2003), Taylor & Francis London
[10] 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, 27, 1-12, (2007) · Zbl 1177.34047
[11] Bohner, M.; Peterson, A., Dynamic equations on time scales: an introduction with applications, (2001), Birkhäuser Boston · Zbl 0978.39001
[12] Bohner, M.; Peterson, A., Advances in dynamic equations on time scales, (2003), Birkhäuser Boston · Zbl 1025.34001
[13] Bohner, M.; Saker, S.H., Oscillation criteria for perturbed nonlinear dynamic equations, Math comput model, 40, 3-4, 249-260, (2004) · Zbl 1112.34019
[14] 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
[15] Erbe, L.; Peterson, A., Boundedness and oscillation for nonlinear dynamic equations on a time scale, Proc amer math soc, 132, 3, 735-744, (2004) · Zbl 1055.39007
[16] Erbe, L.; Peterson, A.; Řehák, P., Comparison theorems for linear dynamic equations on time scales, J math anal appl, 275, 1, 418-438, (2002) · Zbl 1034.34042
[17] Erbe, L.; Peterson, A.; Saker, S.H., Oscillation criteria for second-order nonlinear dynamic equations on time scales, J London math soc, 67, 3, 701-714, (2003) · Zbl 1050.34042
[18] Han, Z.; Sun, S.; Shi, B., Oscillation criteria for a class of second-order emden – fowler delay dynamic equations on time scales, J math anal appl, 334, 2, 847-858, (2007) · Zbl 1125.34047
[19] Hilger, S., Analysis on measure chains — a unified approach to continuous and discrete calculus, Results math, 18, 18-56, (1990) · Zbl 0722.39001
[20] Kusano, T.; Ogata, A.; Usami, H., On the oscillation of solutions of second order quasilinear ordinary differential equations, Hiroshima math J, 23, 3, 645-667, (1993) · Zbl 0797.34030
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.