Oscillation criteria for second order nonlinear neutral dynamic equations on time scales

Article Sidebar

PDF
Published: Mar 31, 2012
DOI: https://doi.org/10.5556/j.tkjm.43.2012.1130
Keywords:
Oscillation second order neutral dynamic equations time scales

Main Article Content

E. Thandapani
Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai
V. Piramanantham
Department of Mathematics, Bharathidasan University, Tiruchirappalli

Abstract

In this paper the authors established some new oscillation criteria for the second order nonlinear neutral delay dynamic equations on time scales. Examples illustrating the main results are given.

Article Details

How to Cite
Thandapani, E., & Piramanantham, V. (2012). Oscillation criteria for second order nonlinear neutral dynamic equations on time scales. Tamkang Journal of Mathematics, 43(1), 109–122. https://doi.org/10.5556/j.tkjm.43.2012.1130
Issue
Vol. 43 No. 1 (2012)
Section
Papers

References

R. P. Agarwal, M. Bohner and A. Peterson, Dynamic

equations on time scales: A survey. J. Comp. Appl .Math., Special issue on dynamic equations on time scales, edited

by R.P.Agarwal, M.Bohner and D.O'Regan (Preprint in Ulmer Seminare 5), 141(2002), (1-2), 1--26,.

D. K. Anderson and A. Zafer, Nonlinear oscillation of second order dynamic equations on time scales, Appl. Math. Let., 22(2009), 1591-1597.

M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhuser, Boston, 2001.

M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhuser, Boston, 2003.

M.Bohner, S.H.Saker, Oscilltion criteria for perturbed nonlinear dynamic equations, Math. Comp. Model., 40(2004), 249--260.

M. Bohner, L. Erbe and A. Peterson, Oscillation for nonlinear second order dynamic equations on a time scales, J. Math. Anal. Appl., 301(2009), 491--507.

L. Erbe, J. Baoguo and A. Peterson, Nonoscillation of second order sublinear dynamic equations on time scales, J. Comp. Appl. Math., 232(2009), 594--599.

L. Erbe, A. Peterson and S. H. Saker, Oscillation criteria for second order nonlinear delay dynamic equations, J. Math. Anal. Appl., 333 (2007), 505--522.

S. R. Grace, R. Agarwal, M. Bohner and D. O'Regan, Oscillation of second order strongly superlinear and strongly sublinear dynamic equations, Comm. Nonl. Sci Num. Sim., 14(2009), 3463--3471.

Z. Han, S. Sun and B. Shi, Oscillation criteria for a calss of second order Emden-Fowler delay dynamic equations on time scales, J. Math. Anal. Appl., 334(2007), 847-858.

S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete analysis, Results Math., 8(1990), 18-56.

M. Huang and W. Feng, Oscillation for forced second order nonlinear dynamic equations on time scales, Elect. J. Diff. Eqn., 145(2005), 1--8.

C. Jinfa, Kamenev type oscillation criteria for delay difference equations, Acta Math. Sci., 27(2007), B(3), 574--580.

I. Kubiczyk, S. H. Saker and J. Morchalo, Kamenev type oscillation criteria for sublinear delay difference equations, Indian J. Pure Appl. Math., 34(2003), (8), 1273--1284.

S. H. Saker, Oscillation of second order nonlinear neutral delay dynamic equations, J. Comp. Appl. Math., 187(2006), 123--141.

S. H. Saker, D. O'Regan and R. P. Agarwal, Oscillation theorems for second order nonlinear neutral delay dynamic equations on time scales, Acta. Math. Sinica, English Series, 24(2007),1409--1432.

Y. Sahiner, Oscillation of second order delay differential equations on time scales}, Nonlinear Analysis: theory, methods and applications, 63(2005), 173--1080.

H. Wu, R. K. Zhuang, and R. M. Mathsen, Oscillation criteria for second-order nonlinear neutral variable delay dynamic equations, Appl. Math. Comp., 178(2006), 321--331.

B. G. Zhang and Z. Shanliang, Oscillation of second order nonlinear delay dynamic equations on time scales, Comp. Math. Appl., 49(2005), 599--609.