Applied and Computational Mathematics

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Oscillation of Second Order Nonlinear Differential Equations with a Damping Term

Received: 23 March 2016    Accepted:     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.

DOI 10.11648/j.acm.20160502.12
Published in Applied and Computational Mathematics (Volume 5, Issue 2, April 2016)
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), 2024. Published by Science Publishing Group

Keywords

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

References
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[5] S. P. Rogovchenko, Y. V. Rogovchenko, “Oscillation results for general second-order differential equations with damping term,” J. Math. Anal. Appl. 279 (2003) 139-152.
[6] Y. V. Rogovchenko, Tuncay F., “Oscillation criteria for second-order nonlinear differential equations with damping,” Nonlinear Anal. 69 (2008) 208-221.
[7] Y. V. Rogovchenko, F. Tuncay, “Oscillation theorems for a class of second order nonlinear differential equations with damping,” Taiwanese J. Math.13 (2009) 1909-1928.
[8] M. Kirane and Y. V. Rogovchenko, “On oscillation of nonlinear second order differential equation with damping term,” Appl. Math. Comput., 117 (2001) 177-192.
[9] T. X. Li, Y. V. Rogovchenko, S. H. Tang., “Oscillation criteria for second-order nonlinear differential equations with damping,” Math. Slovaca 64(2014) No. 5, 1227-1236.
[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.
[12] J. Yan, “Oscillation theorems for second order linear differential equations with damping,” Proc. Amer. Math. Soc. 98 (1986) 276-282.
[13] C. C. Yeh, “Oscillation theorems for nonlinear second order differential equations with damping term,” Proc. Amer. Math. Soc. 84 (1982) 397-402.
[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.
[15] S. R. Grace, B. S. Lalli, C. C. Yeh, “Oscillation theorems for nonlinear second order differential equations with a nonlinear damping term,” SIAM J. Math. Anal. 15 (1984) 1082-1093.
[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.
[18] E. Tunc, H. Avci, “Oscillation criteria for a class of second order nonlinear differential equations with damping,” Bulletin of Mathematical Analysis and Applications. 4 (2012) 40-50.
[19] E. Tunc, “A note on the oscillation of second order differential equations with damping,” J. Comput. Anal. Appl. 12 (2010) 444-453.
[20] E. Tunc, H. Avci, “New oscillation theorems for a class of second order damped nonlinear differential equations,” Ukrainian Math. J. 63 (2012) 1441-1457.
[21] A. A. Salhin, U. K. S. Din, R. R. Ahmad, M. S. M. Noorani, “Some oscillation criteria for a class of second order nonlinear damped differential equations,” Applied Mathematics and Computation, 247 (2014) 962-968.
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Author Information
  • School of Mathematics and System Sciences, Shenyang Normal University, Shenyang, Liaoning, P. R. China

  • School of Mathematics and System Sciences, Shenyang Normal University, Shenyang, Liaoning, P. R. China; School of Mathematics, Jilin University, Changchun, Jilin, P. R. China

  • 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

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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://download.sciencepg.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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    AU  - Desheng Li
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    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
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