IJPAM: Volume 116, No. 2 (2017)

Title

OSCILLATION CRITERIA FOR SECOND ORDER
NONLINEAR NEUTRAL DELAY DYNAMIC
EQUATIONS ON TIME SCALES

Authors

M.M.A. El-Sheikh$^1$, R.A. Sallam$^2$, A.M. Hassan$^3$
$^{1,2,3}$Department of Mathematics
Faculty of Science
Menoufia University
Shebeen EL-Koom, EGYPT

Abstract

The purpose of this paper is to obtain new sufficient conditions for the oscillation of solutions of a class of second-order neutral delay dynamic equations. The obtained results improve and extend some known results in the literature. Three examples are given to illustrate the main results.

History

Received: 2017-01-09
Revised: 2017-08-30
Published: October 7, 2017

AMS Classification, Key Words

AMS Subject Classification: 34C10, 34K11
Key Words and Phrases: oscillation, second order, dynamic equations, neutral delay equations, time scales

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Bibliography

1
M. Bohner, A. Peterson, Dynamic Equations on Time-Scales: An Introduction with Applications, Birkhauser, Boston, 2001.

2
M.M.A. El-Sheikh, R.A. Sallam, Nahed M. Mohamady, Oscillation criteria for second order nonlinear neutral differential equations, Differential Equations and Control Processes, 3 (2011), 1-17.

3
M.M.A. El-Sheikh, R.A. Sallam, Nahed M. Mohamady, New criteria for oscillation of second order nonlinear dynamic equations with damping on time scales, IJRANSS, 3, No. 3 (2015), 79-86.

4
S. Hilger, Analysis on measure chain-a unified approach to continuous and discrete calculus, Results Math., 18 (1990), 18-56.

5
Jingjing Wang, M.M.A. El-Sheikh, R.A. Sallam, D.I. Elimy, Li Tongxing, Oscillation results for nonlinear second-order damped dynamic equations, J. Nonlinear Sci. Appl., 8 (2015), 877-883.

6
John R. Graef, E. Tunc, Oscillation criteria for second order functional dynamic equations on time scales, IEJPAM, 8 (2014), 17-31.

7
Lynn Erbe, Taher Hassan, Allan Peterson, Oscillation of second order functional dynamic equations, International Journal of Difference Equations, 5 (2010), 175–193.

8
Luhong Ye, Zhiting Xu, Oscillation criteria for second order quasilinear neutral delay differential equations, Applied Mathematics and Computation, 207 (2009), 388-396.

9
Ravi P. Agarwal, Donal O'Regan, S.H. Saker, Oscillation criteria for second-order nonlinear neutral delay dynamic equations, J. Math. Anal. Appl., 300 (2004), 203-217.

10
R. Xu, F. Meng, New Kamenev-type oscillation criteria for second order neutral nonlinear differential equations, Applied Mathematics and Computation, 188 (2007), 1364-1370.

11
R.A. Sallam, New oscillation criteria for second order nonlinear delay differential equations,International Journal of Nonlinear science, 12 (2011), 3-11.

12
S.H. Saker, Oscillation criteria of second-order half-linear dynamic equations on time scales, Journal of Computational and Applied Mathematics, 177 (2005), 375-387.

13
S.H. Saker , Donal O'Regan, New oscillation criteria for second-order neutral dynamic equations on time scales via Riccati substitution, Hiroshima Math. J., 42 (2012) 77-98.

14
Zhang Shao-Yan, Wang Qi-Ru, Oscillation of second order nonlinear neutral dynamic equations on time scales, Applied Mathematics and Computation, 216 (2010), 2837-2848.

15
A.A. Soliman, R.A. Sallam, A.M. Hassan, Oscillation criteria of second order nonlinear neutral differential equations, IJAMR, 3 (2012), 314-322.

16
Li Tongxing, Thandapani Ethiraju, Oscillation of solutions to second-order neutral differential equations, Electronic J. of Differential Equations, 67 (2014), 1-7.

17
R. Xu, F. Meng, Oscillation criteria for second order quasi-linear neutral delay differential equations, Appl. Math. Comput., 192 (2007), 216-222.

How to Cite?

DOI: 10.12732/ijpam.v116i2.4 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 2
Pages: 329 - 342


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