Volume 2014, Issue 1 545189

Research Article

Open Access

Set of Oscillation Criteria for Second Order Nonlinear Forced Differential Equations with Damping

Corresponding Author

Ambarka Abdalla Salhin

[email protected]

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia ukm.my

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Ummul Khair Salma Din,

Ummul Khair Salma Din

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia ukm.my

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Rokiah Rozita Ahmad,

Rokiah Rozita Ahmad

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia ukm.my

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Mohd Salmi Md Noorani,

Mohd Salmi Md Noorani

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia ukm.my

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Ambarka Abdalla Salhin,

Corresponding Author

Ambarka Abdalla Salhin

[email protected]

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia ukm.my

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Ummul Khair Salma Din,

Ummul Khair Salma Din

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia ukm.my

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Rokiah Rozita Ahmad,

Rokiah Rozita Ahmad

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia ukm.my

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Mohd Salmi Md Noorani,

Mohd Salmi Md Noorani

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia ukm.my

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First published: 02 September 2014

https://doi.org/10.1155/2014/545189

Academic Editor: Qi-Ru Wang

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Abstract

By employing a generalized Riccati technique and an integral averaging technique, some new oscillation criteria are established for the second order nonlinear forced differential equation with damping. These results extend, improve, and unify some known oscillation criteria in the existing literature.

References

1 Coles W. J., An oscillation criteria for second order differential equations, Proceedings of the American Mathematical Socie. (1968) 19, 755–759.
10.1090/S0002-9939-68-99981-4
Web of Science® Google Scholar
2 Elabbasy E. M. and Elsharabasy M. A., Oscillation properties for second order nonlinear differential equations, Kyungpook Mathematical Journal. (1997) 37, no. 2, 211–220, MR1487805, ZBL0901.34040.
Google Scholar
3 Kamenev I. V., An integral criterion for oscillation of linear differential equations of second order, Mathematical Notes of the Academy of Sciences of the USSR. (1978) 23, no. 2, 136–138, https://doi.org/10.1007/BF01153154, 2-s2.0-3242779415.
10.1007/BF01153154
Google Scholar
4 Lu F. and Meng F., Oscillation theorems for superlinear second-order damped differential equations, Applied Mathematics and Computation. (2007) 189, no. 1, 796–804, https://doi.org/10.1016/j.amc.2006.11.175, MR2330256, ZBL1128.34020, 2-s2.0-34248385329.
10.1016/j.amc.2006.11.175
Web of Science® Google Scholar
5 Philos C. G., Oscillation of sublinear differential equations of second order, Nonlinear Analysis. Theory, Methods & Applications. (1983) 7, no. 10, 1071–1080, https://doi.org/10.1016/0362-546X(83)90016-0, MR719359, 2-s2.0-0020833751.
10.1016/0362-546X(83)90016-0
Web of Science® Google Scholar
6 Rogovchenko Y. V. and Tuncay F., Oscillation theorems for a class of second order nonlinear differential equations with damping, Taiwanese Journal of Mathematics. (2009) 13, no. 6, 1909–1928, MR2583528, 2-s2.0-74249121619.
10.11650/twjm/1500405648
Web of Science® Google Scholar
7 Salhin A. A., Din U. K. S., Ahmad R. R., and Noorani M. S., Oscillation criteria of second order nonlinear differential equations with variable coefficients, Discrete Dynamics in Nature and Society. (2014) 2014, 9, 279236, https://doi.org/10.1155/2014/279236.
10.1155/2014/279236
Web of Science® Google Scholar
8 Wang Q.-R., Oscillation criteria for nonlinear second order damped differential equations, Acta Mathematica Hungarica. (2004) 102, no. 1-2, 117–139, https://doi.org/10.1023/B:AMHU.0000023211.53752.03, MR2038173, 2-s2.0-8144223363.
10.1023/B:AMHU.0000023211.53752.03
Web of Science® Google Scholar
9 Wang X. j. and Song G. h., Oscillation criteria for a second-order nonlinear damped differential equation, International Journal of Information & Systems Sciences. (2011) 7, no. 1, 73–82, MR2801840.
CAS Google Scholar
10 Wang X. J. and Song G. H., Oscillation theorems for a class of nonlinear second order differential equations with damping, Advances in Pure Mathimatics. (2013) 3, 226–233, https://doi.org/10.4236/apm.2013.31A032.
10.4236/apm.2013.31A032
Google Scholar
11 Zhang M. and Song G. H., Oscillation theorems for second-order nonlinear perturbed differential equations with damping, Journal of Shanghai University. (2011) 15, no. 6, 510–516, https://doi.org/10.1007/s11741-011-0777-1, MR2870454, 2-s2.0-84862971744.
10.1007/s11741-011-0777-1
Google Scholar

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Set of Oscillation Criteria for Second Order Nonlinear Forced Differential Equations with Damping

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Set of Oscillation Criteria for Second Order Nonlinear Forced Differential Equations with Damping

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