Oscillation criteria for a certain class of second order Emden-fowler dynamic equations

Electronic Transactions on Numerical Analysis

Volumn 27, Issue , 2007, Pages 1-12

  Akin Bohner, Elvan ^a   Bohner, Martin ^a   Saker, Samir H ^b  

^a MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (United States)

^b MANSOURA UNIVERSITY   (Egypt)

Author keywords

Dynamic equation; Oscillation; Riccati transformation technique; Time scale

Indexed keywords

DYNAMIC MODELS; MATHEMATICAL TRANSFORMATIONS; RICCATI EQUATIONS;

DYNAMIC EQUATIONS; OSCILLATION CRITERIA; RICCATI TRANSFORMATION TECHNIQUE;

OSCILLATORS (ELECTRONIC);

EID: 37249030980     PISSN: None     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (24)

1. R. P. AGARWAL, M. BOHNER, D. O'REGAN, AND A. PETERSON, Dynamic equations on time scales: A survey, J. Comput. Appl. Math., 141 (2002), pp. 1-26.
2. E. AKIN, L. ERBE, B. KAYMAKÇALAN, AND A. PETERSON, Oscillation results for a dynamic equation on a time scale, J. Differ. Equations Appl., 7 (2001), pp. 793-810.
3. E. AKIN-BOHNER AND J. HOFFACKER, Oscillation properties of an Emden-Fowler type equation on discrete time scales, J. Difference Equ. Appl., 9 (2003), pp. 603-612.
4. _, Solution properties on discrete time scales, J. Difference Equ. Appl., 9 (2003), pp. 63-75.
5. F. V. ATKINSON, On second-order non-linear oscillations, Pacific J. Math., 5 (1955), pp. 643-647.
6. S̃. BELOHOREC, Non-linear oscillations of a certain non-linear second-order differential equation, Mat. Fyz. Časopis Sloven. Akad. Vied, 12 (1962), pp. 253-262.
7. M. BOHNER, O. DOŠLÝ, AND W. KRATZ, An oscillation theorem for discrete eigenvalue problems, Rocky Mountain J. Math., 33 (2003), pp. 1233-1260.
8. M. BOHNER AND G. S. GUSEINOV, Improper integrals on time scales, Dynam. Systems Appl., 12 (2003), pp. 45-66.
9. M. BOHNER AND A. PETERSON, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001.
10. _, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
11. M. BOHNER AND S. H. SAKER, Oscillation criteria for perturbed nonlinear dynamic equations, Math. Comput. Modelling, 40 (2004), pp. 249-260.
12. _, Oscillation of second order nonlinear dynamic equations on time scales, Rocky Mountain J. Math., 34 (2004), pp. 1239-1254.
13. O. DOŠLÝ AND S. HILGER, A necessary and sufficient condition for oscillation of the Sturm-Liouville dynamic equation on time scales, J. Comput. Appl. Math., 141 (2002), pp. 147-158.
14. L. ERBE, Oscillation criteria for second order linear equations on a time scale, Canad. Appl. Math. Quart., 9 (2001), pp. 345-375.
15. L. ERBE AND A. PETERSON, Positive solutions for a nonlinear differential equation on a measure chain, Math. Comput. Modelling, 32 (2000), pp. 571-585.
16. _, Riccati equations on a measure chain, in Proceedings of Dynamic Systems and Applications (Atlanta, GA, 1999), G. S. Ladde, N. G. Medhin, and M. Sambandham, eds., vol. 3, Dynamic publishers, Atlanta, GA, 2001, pp. 193-199.
17. _, Oscillation criteria for second order matrix dynamic equations on a time scale, J. Comput. Appl. Math., 141 (2002), pp. 169-185.
18. L. ERBE, A. PETERSON, AND P. ŘEHÁ K, Comparison theorems for linear dynamic equations on time scales, J. Math. Anal. Appl., 275 (2002), pp. 418-438.
19. 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), pp. 701-714.
20. S. HILGER, Analysis on measure chains -a unified approach to continuous and discrete calculus, Results Math., 18 (1990), pp. 18-56.
21. S. HUFF, G. OLUMOLODE, N. PENNINGTON, AND A. PETERSON, Oscillation of anEuler-Cauchy dynamic equation, in Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, Wilmington, 2002, pp. 24-27.
22. I. V. KAMENEV, An integral criterion for oscillation of linear differential equations of second order, Mat. Zametki, 23 (1978), pp. 249-251.
23. S. H. SAKER, Oscillation of nonlinear dynamic equations on time scales, Appl. Math. Comput., 148 (2004), pp. 81-91.
24. J. S. W. WONG, On the generalized Emden-Fowler equation, SIAM Rev., 17 (1975), pp. 339-360.