Oscillation of Second Order Nonlinear Differential Equations with a Damping Term

Xue Mi; Ying Huang; Desheng Li

doi:doi:10.11648/j.acm.20160502.12

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Oscillation of Second Order Nonlinear Differential Equations with a Damping Term

Xue Mi, Ying Huang, Desheng Li

Published in Applied and Computational Mathematics (Volume 5, Issue 2)

Received: 23 March 2016 Published: 25 March 2016

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Abstract

A class of second-order nonlinear differential equations with a damping term is investigated in this paper. By using the Riccati transformation technique and general weight functions, we obtain some new sufficient conditions for the oscillation of the equation. Our results improve and extend some known results. Two examples are given to illustrate the main results.

Published in	Applied and Computational Mathematics (Volume 5, Issue 2)
DOI	10.11648/j.acm.20160502.12
Page(s)	46-50
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Oscillation, Second Order Nonlinear Differential Equation, Damping Term, Riccati Transformation Technique, Weight Function

References

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[4]	S. P. Rogovchenko, Y. V. Rogovchenko, “Oscillation of differential equations with damping,” Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 10 (2003) 447-461.
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[6]	Y. V. Rogovchenko, Tuncay F., “Oscillation criteria for second-order nonlinear differential equations with damping,” Nonlinear Anal. 69 (2008) 208-221.
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[10]	J. S. W. Wong, “On Kamenev-type oscillation for second order differential equations with damping,” J. Math. Anal. Appl. 248 (2001) 244-257.
[11]	J. Yan, “A note on an oscillation criterion for an equation with damped term,” Proc. Amer. Math. Soc. 90 (1984) 277-280.
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[14]	S. R. Grace, B. S. Lalli, “Oscillation theorems for second order superlinear differential equations with damping,” J. Austral. Math. Soc. Ser. A 53(1992) 156-165.
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[16]	S. R. Grace, B. S. Lalli, C. C. Yeh, “Addendum: Oscillation theorems for nonlinear second order differential equations with a nonlinear damping term,” SIAM J. Math. Anal. 19 (1988) 1252-1253.
[17]	X. J. Wang, G. H. Song, “Oscillation Theorems for a class of nonlinear second order differential equations with damping,” Advances in Pure Mathematics. 3(2013) 226-233.
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APA Style

Xue Mi, Ying Huang, Desheng Li. (2016). Oscillation of Second Order Nonlinear Differential Equations with a Damping Term. Applied and Computational Mathematics, 5(2), 46-50. https://doi.org/10.11648/j.acm.20160502.12

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ACS Style

Xue Mi; Ying Huang; Desheng Li. Oscillation of Second Order Nonlinear Differential Equations with a Damping Term. Appl. Comput. Math. 2016, 5(2), 46-50. doi: 10.11648/j.acm.20160502.12

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AMA Style

Xue Mi, Ying Huang, Desheng Li. Oscillation of Second Order Nonlinear Differential Equations with a Damping Term. Appl Comput Math. 2016;5(2):46-50. doi: 10.11648/j.acm.20160502.12

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@article{10.11648/j.acm.20160502.12,
  author = {Xue Mi and Ying Huang and Desheng Li},
  title = {Oscillation of Second Order Nonlinear Differential Equations with a Damping Term},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {2},
  pages = {46-50},
  doi = {10.11648/j.acm.20160502.12},
  url = {https://doi.org/10.11648/j.acm.20160502.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160502.12},
  abstract = {A class of second-order nonlinear differential equations with a damping term is investigated in this paper. By using the Riccati transformation technique and general weight functions, we obtain some new sufficient conditions for the oscillation of the equation. Our results improve and extend some known results. Two examples are given to illustrate the main results.},
 year = {2016}
}

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TY  - JOUR
T1  - Oscillation of Second Order Nonlinear Differential Equations with a Damping Term
AU  - Xue Mi
AU  - Ying Huang
AU  - Desheng Li
Y1  - 2016/03/25
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160502.12
DO  - 10.11648/j.acm.20160502.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 46
EP  - 50
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20160502.12
AB  - A class of second-order nonlinear differential equations with a damping term is investigated in this paper. By using the Riccati transformation technique and general weight functions, we obtain some new sufficient conditions for the oscillation of the equation. Our results improve and extend some known results. Two examples are given to illustrate the main results.
VL  - 5
IS  - 2
ER  -

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Author Information

Xue Mi

School of Mathematics and System Sciences, Shenyang Normal University, Shenyang, Liaoning, P. R. China
Ying Huang

School of Mathematics and System Sciences, Shenyang Normal University, Shenyang, Liaoning, P. R. China
Desheng Li

School of Mathematics and System Sciences, Shenyang Normal University, Shenyang, Liaoning, P. R. China

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APA Style

Xue Mi, Ying Huang, Desheng Li. (2016). Oscillation of Second Order Nonlinear Differential Equations with a Damping Term. Applied and Computational Mathematics, 5(2), 46-50. https://doi.org/10.11648/j.acm.20160502.12

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ACS Style

Xue Mi; Ying Huang; Desheng Li. Oscillation of Second Order Nonlinear Differential Equations with a Damping Term. Appl. Comput. Math. 2016, 5(2), 46-50. doi: 10.11648/j.acm.20160502.12

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AMA Style

Xue Mi, Ying Huang, Desheng Li. Oscillation of Second Order Nonlinear Differential Equations with a Damping Term. Appl Comput Math. 2016;5(2):46-50. doi: 10.11648/j.acm.20160502.12

Copy | Download

@article{10.11648/j.acm.20160502.12,
  author = {Xue Mi and Ying Huang and Desheng Li},
  title = {Oscillation of Second Order Nonlinear Differential Equations with a Damping Term},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {2},
  pages = {46-50},
  doi = {10.11648/j.acm.20160502.12},
  url = {https://doi.org/10.11648/j.acm.20160502.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160502.12},
  abstract = {A class of second-order nonlinear differential equations with a damping term is investigated in this paper. By using the Riccati transformation technique and general weight functions, we obtain some new sufficient conditions for the oscillation of the equation. Our results improve and extend some known results. Two examples are given to illustrate the main results.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Oscillation of Second Order Nonlinear Differential Equations with a Damping Term
AU  - Xue Mi
AU  - Ying Huang
AU  - Desheng Li
Y1  - 2016/03/25
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160502.12
DO  - 10.11648/j.acm.20160502.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 46
EP  - 50
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20160502.12
AB  - A class of second-order nonlinear differential equations with a damping term is investigated in this paper. By using the Riccati transformation technique and general weight functions, we obtain some new sufficient conditions for the oscillation of the equation. Our results improve and extend some known results. Two examples are given to illustrate the main results.
VL  - 5
IS  - 2
ER  -

Copy | Download