OSCILLATION OF SECOND ORDER DELAY DYNAMIC EQUATIONS WITH OSCILLATORY COEFFICIENTS

TitleOSCILLATION OF SECOND ORDER DELAY DYNAMIC EQUATIONS WITH OSCILLATORY COEFFICIENTS
Publication TypeJournal Article
Year of Publication2010
AuthorsWANG, BIYING, XU, ZHITING
Secondary TitleCommunications in Applied Analysis
Volume1
Issue4
Start Page525
Pagination540
Date Published12/2010
Type of Workscientific: mathematics
ISSN1083–2564
AMS34C10, 34K11, 39A11, 39A13.
Abstract
In this paper, we extend the oscillation criteria established by Fite, Kamenev, Hille and Nehari for second order linear differential equations to second order linear delay dynamic equations with oscillatory coefficients on time scales. Our results are essentially new even for second order differential equations and difference equations. Finally we consider several examples to illustrate our main theorems.
URLhttp://www.acadsol.eu/en/articles/14/4/9.pdf
Short TitleDYNAMIC EQUATIONS WITH OSCILLATORY COEFFICIENTS
Refereed DesignationRefereed
Full Text

REFERENCES

[1] R.P. Agarwal, M. Bohner, D. O’Regan, A. Peterson, Dynamic equations on time scales: A survey, J. Comput. Appl. Math. 141(1-2) (2002), 1–26.
[2] R.P. Agarwal, M. Bohner, S. H. Saker, Oscillation of second order delay dynamic equations, Can. Appl. Math. Quart. 13 (2005), 1–17.
[3] D.R. Anderson, Oscillation of second-order forced functional dynamic equations with oscillatory potentials, J. Difference Equ. Appl. 13 (2007), 407–421.
[4] M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhauser, Boston, 2001.
[5] M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkh ̈auser, Boston, 2003.
[6] L. Erbe, T. S. Hassan, A. Peterson, Oscillation criteria for nonlinear damped dynamic equations on time scales, Appl. Math. Comput. 203 (2008), 343–357.
[7] L. Erbe, T. S. Hassan, A. Peterson, S.H. saker, Oscillation criteria for half-linear delay dynamic equations on time scales, Nonlinear Dyn. Syst. Theory. (1)9 (2009), 51–68.
[8] L. Erbe, A. Peterson, S.H. Saker, Kamenev-type oscillation criteria for second order linear delay dynamic equations, Dynam. Systems. Appl. 15 (2006), 65–78.
[9] L. Erbe, A. Peterson, S.H. Saker, Oscillation criteria for second-order nonlinear delay dynamic equations, J. Math. Anal. Appl. 333 (2007), 505–522.
[10] W.B. Fite, Concerning the zeros of the solutions of certain differential equations, Trans. Amer. Math. Soc. 19 (1918), 341–352.
[11] Z. Han, B. Shi, S. Sun, Oscillation criteria for second order delay dynamic equations on time scales, Adv. Difference Equ. Vol 2007. Article ID 70730, 16 page.
[12] Z. Han, S. Sun, B. Shi, Oscillation criteria for a class of second-order Emden-Fowler delay dynamic equations on time scales, J. Math. Anal. Appl. 334 (2007), 847–858.
[13] G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities, Second ed. Cambridge University Press, Cambridge, 1952.
[14] S. Hilger, Analysis on measure chains – a unified approach to continuous and discrete calculus, Results Math. 18 (1990), 18–56.
[15] E. Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948), 234–252.
[16] I.V. Kamenev, An integral criterion for oscillation of linear differential equations of second order, Mat. Zametki. 23 (1978), 249–251.
[17] S. Nehari, Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957), 428–445.
[18] Y. Sahiner, Oscillation of second-order delay differential equations on time scales, Nonlinear Anal. 63 (2005), 1073–1080.
[19] B.G. Zhang, S. Zhu, Oscillation of second-order nonlinear delay dynamic equations on time scales, Comput. Math. Appl. 49 (2005), 599–609.