Oscillation criteria of second-order half-linear dynamic equations on time scales

Journal of Computational and Applied Mathematics

Volumn 177, Issue 2, 2005, Pages 375-387

  Saker, S H ^a  

^a Mansoura University   (Egypt)

Author keywords

Oscillation; Second order half linear dynamic equations; Time scale

Indexed keywords

DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; OSCILLATIONS; RICCATI EQUATIONS;

SECOND ORDER HALF LINEAR DYNAMIC EQUATIONS; TIME SCALE;

LINEAR EQUATIONS;

EID: 13844254252     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.09.028     Document Type: Article

References (20)

1. R.P. Agarwal, M. Bohner, D. O'Regan, A. Peterson, Dynamic equations on time scales: A survey, in: R.P. Agarwal, M. Bohner, D. O'Regan (Eds.), Dynamic Equations on Time Scales (Preprint in Ulmer Seminare 5), J. Comput. Appl. Math. 141 (2002) 1-26 (special issue).
2. E. Akin L. Erbe B. Kaymakçalan A. Peterson Oscillation results for a dynamic equation on a time scale J. Differential Equations Appl. 7 (2001) 793-810
3. E.A. Bohner J. Hoffacker Oscillation properties of an Emden-Fowler type equations on discrete time scales J. Differential Equations Appl. 9 (2003) 603-612
4. M. Bohner A. Peterson Dynamic Equations on Time Scales An Introduction with Applications Birkhäuser Boston 2001
5. M. Bohner A. Peterson Advances in Dynamic Equations on Time Scales Birkhäuser Boston 2003
6. M. Bohner S.H. Saker Oscillation of second order nonlinear dynamic equations on time scales Rocky Mountain J. Math. 34 (2004) 1239-1254
7. M. Bohner, S.H. Saker, Oscillation criteria for perturbed nonlinear dynamic equations, Math. Comp. Modelling, in press.
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.), Dynamic Equations on Time Scales, J. Comp. Appl. Math. 141 (1-2) (2002) 147-158 (special issue).
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 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, Dynamic Publishers, Atlanta, 2001, pp. 193-199.
12. L. Erbe, A. Peterson, Oscillation criteria for second-order matrix dynamic equations on a time scale, in: R.P. Agarwal, M. Bohner, D. O'Regan (Eds.), Dynamic Equations on Time Scales, J. Comput. Appl. Math. 141 (2002) 169-185 (special issue).
13. L. Erbe A. Peterson Boundedness and oscillation for nonlinear dynamic equations on a time scale Proc. Amer. Math. Soc. 32 (2004) 735-744
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.), 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 Results Math. 18 (1990) 18-56
17. I.V. Kamenev An integral criterion for oscillation of linear differential equations of second order Mat. Zametki 23 (1978) 249-251
18. S.H.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, 2002, pp. 24-27.
19. S.H. Saker Oscillation of nonlinear dynamic equations on time scales Appl. Math. Comput. 148 (2004) 81-91
20. E. Thandapani K. Ravi J.R. Graef Oscillation and comparison theorems for half-linear second-order difference equations Comput. Math. Appl. 42 (2001) 953-960