Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales

Journal of Computational and Applied Mathematics

Volumn 181, Issue 1, 2005, Pages 92-102

  Erbe, L ^a   Peterson, A ^a   Saker, S H ^b  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^b Mansoura University   (Egypt)

Author keywords

Oscillation; Riccati transformation technique; Third order nonlinear dynamic equation; Time scale

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; INTEGRAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; THEOREM PROVING;

RICCATI TRANSFORMATION TECHNIQUE; THIRD ORDER NONLINEAR DYNAMIC EQUATION; TIME SCALE;

NONLINEAR EQUATIONS;

EID: 19444376939     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.11.021     Document Type: Article

References (19)

1. R.P. Agarwal S.R. Grace D. O'Regan Oscillation Theory for Difference and Functional Differential Equations 2000 Kluwer Academic Publishers Dordrecht
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. E.A. Bohner J. Hoffacker Oscillation properties of an Emden-Fowler type equation on discrete time scales J. Differential Equations Appl. 9 2003 603-612
4. M. Bohner O. Došlý W. Kratz An oscillation theorem for discrete eigenvalue problems Rocky Mountain J. Math. 33 4 2003 1233-1260
5. M. Bohner A. Peterson Dynamic Equations on Time Scales: An Introduction with Applications 2001 Birkhäuser Boston
6. M. Bohner S.H. Saker Oscillation of second order nonlinear dynamic equations on time scales Rocky Mountain J. Math. 34 4 2004 1239-1254
7. M. Bohner, S.H. Saker, Oscillation criteria for perturbed nonlinear dynamic equations, submitted for publication.
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.
9. L. Erbe Oscillation criteria for second order linear equations on a time scale Canad. Appl. Math. Quart. 9 2001 1-31
10. L. Erbe A. Peterson Positive solutions for a nonlinear differential equation on a measure chain Math. Comput. Modelling, Boundary Value Problems and Related Topics 32 2000 571-585
11. L. Erbe A. Peterson Riccati equations on a measure chain, in: G.S. Ladde N.G. Medhin M. Sambandham (Eds.), Proceedings of Dynamic Systems and Applications vol. 3 2001 Dynamic publishers Atlanta 193-199
12. L. Erbe A. Peterson Boundedness and oscillation for nonlinear dynamic equations on a time scale Proc. Amer. Math. Soc. 132 2004 735-744
13. L. Erbe A. Peterson P. Rehak Comparison theorems for linear dynamic equations on time scales J. Math. Anal. Appl. 275 2002 418-438
14. L. Erbe A. Peterson S.H. Saker Oscillation criteria for second-order nonlinear dynamic equations on time scales J. London Math. Soc. 67 2003 701-714
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.
16. S. Hilger Analysis on measure chains - a unified approach to continuous and discrete calculus Resultate Math. 18 1990 18-56
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.
18. I.V. Kamenev An integral criterion for oscillation of linear differential equations of second order Mat. Zametki 23 1978 249-251
19. S.H. Saker Oscillation of nonlinear dynamic equations on time scales Appl. Math. Comput. 148 2004 81-91