OSCILLATION OF CERTAIN DYNAMIC EQUATIONS ON TIME SCALES

TitleOSCILLATION OF CERTAIN DYNAMIC EQUATIONS ON TIME SCALES
Publication TypeJournal Article
Year of Publication2015
AuthorsHIGGINS, RAEGAN
Volume19
Issue1
Start Page113
Pagination15
Date Published2015
ISSN1083-2564
AMS34K11, 39A10, 39A99
Abstract

Oscillation criteria are established for second-order nonlinear nabla dynamic equations on an isolated time scale ${ \mathbb{T} }$. Our main goal is to establish a relationship between the oscillatory behavior of these equations. We also give two results about the behavior of a second-order self-adjoint equation with mixed derivatives on a time scale that is unbounded above. We use the Riccati transformation technique to obtain our results.
URLhttp://www.acadsol.eu/en/articles/19/1/9.pdf
Refereed DesignationRefereed
Full Text

.
REFERENCES
[1] M. Bohner and G. S. Guseinov, Improper integrals on time scales, Dynam. Systems Appl 12 (2003), 45–65.
[2] M. Bohner and A. Peterson (eds.), Advances in Dynamic Equations on Time Scales, Birkh¨auser Boston Inc., Boston, 2003.
[3] M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser Boston Inc., Boston, 2001.
[4] L. H. Erbe, Q. Kong and B. G. Zhang, Oscillation Theory for Functional Differential Equations,
Marcel Dekker, New Yorks, 1995.
[5] L. Erbe, A. Peterson and P. Reh´ak, Comparison theorems for linear dynamic equations o ˇ n
time scales, J. Math. Anal. Appl. 275 (2002) 418–438.
[6] R. Higgins, Oscillation results for second-order delay dynamic equations, Int. J. Difference Equ. 5 (2010), 41–54.
[7] S. Hilger, Analysis on measure chains—a unified approach to continuous and discrete calculus, Results Math. 18 (1990), 18–56.
[8] S. H. Saker, Oscillation of nonlinear dynamic equations on time scales, Appl. Math. Comput.
148 (2004), 81–91.
[9] J. Yan, Oscillation theoresm for linear second order differential equations, Acta Math. Appl.
Sinica 10(2) (1987), 167–174.
[10] B. G. Zhang and Z. Shanliang, Oscillation of second-order nonlinear delay dynamic equations
on time scales, Comput. Math. Appl. 49 (2005), 599–6