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OSCILLATION CRITERIA FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS

Year 2016, Volume: 29 Issue: 4, 923 - 927, 19.12.2016

Abstract

 

In this paper, we are concerned with the oscillation of a class of second order nonlinear differential equations. By using the Riccati technique, some new oscillation criteria established which generalize and extend a number of existing oscillation criteria. Example is also given to illustrate our results.

References

  • Fite, W.B., Concerning the zeros of the solutions of
  • certian differential equations, Trans. Amer. Math.
  • Soc. 19 (1918), 341–352.
  • Wintner, A., A criterion of oscillatory stability,
  • Quart. Appl. Math. 7 (1949), 15–117.
  • Hartman, P., Non-oscillatory linear differential
  • equations of second order, Amer. J. Math. 74
  • (1952), 389–400.
  • Kamenev, I.V., Integral criterion for oscillation of
  • linear differential equations of second order, Math.
  • Zametki 23 (1978), 249–251.
  • Wong, F.H., Yeh, C.C.: Oscillation criteria for
  • second order super-linear differential equations,
  • Math. Japonica 37 (1992), 573–584.
  • Bihari, I., An oscillation theorem concerning the half
  • linear differential equation of the second order,
  • Magyar Tud. Akad. Mat. Kutato Int. Kozl. 8
  • (1963), 275–280.
  • Kartsatos, A.G., On oscillation of nonlinear
  • equations of second order, J. Math. Anal. Appl. 24
  • (1968), 665–668.
  • Elabbasy, E.M., Elzeiny, Sh. R., Oscillation
  • theorems concerning non-linear differential
  • equations of the second order, Opuscula
  • Mathematica, Vol. 31, No. 3, (2011), 373-391.
  • Bartle, R.G., The elements of real analysis, 7th ed.,
  • John Wiley and Sons, 233 (1976).
Year 2016, Volume: 29 Issue: 4, 923 - 927, 19.12.2016

Abstract

References

  • Fite, W.B., Concerning the zeros of the solutions of
  • certian differential equations, Trans. Amer. Math.
  • Soc. 19 (1918), 341–352.
  • Wintner, A., A criterion of oscillatory stability,
  • Quart. Appl. Math. 7 (1949), 15–117.
  • Hartman, P., Non-oscillatory linear differential
  • equations of second order, Amer. J. Math. 74
  • (1952), 389–400.
  • Kamenev, I.V., Integral criterion for oscillation of
  • linear differential equations of second order, Math.
  • Zametki 23 (1978), 249–251.
  • Wong, F.H., Yeh, C.C.: Oscillation criteria for
  • second order super-linear differential equations,
  • Math. Japonica 37 (1992), 573–584.
  • Bihari, I., An oscillation theorem concerning the half
  • linear differential equation of the second order,
  • Magyar Tud. Akad. Mat. Kutato Int. Kozl. 8
  • (1963), 275–280.
  • Kartsatos, A.G., On oscillation of nonlinear
  • equations of second order, J. Math. Anal. Appl. 24
  • (1968), 665–668.
  • Elabbasy, E.M., Elzeiny, Sh. R., Oscillation
  • theorems concerning non-linear differential
  • equations of the second order, Opuscula
  • Mathematica, Vol. 31, No. 3, (2011), 373-391.
  • Bartle, R.G., The elements of real analysis, 7th ed.,
  • John Wiley and Sons, 233 (1976).
There are 27 citations in total.

Details

Journal Section Mathematics
Authors

Adil Mısır

Süleyman Öğrekçi

Publication Date December 19, 2016
Published in Issue Year 2016 Volume: 29 Issue: 4

Cite

APA Mısır, A., & Öğrekçi, S. (2016). OSCILLATION CRITERIA FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS. Gazi University Journal of Science, 29(4), 923-927.
AMA Mısır A, Öğrekçi S. OSCILLATION CRITERIA FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS. Gazi University Journal of Science. December 2016;29(4):923-927.
Chicago Mısır, Adil, and Süleyman Öğrekçi. “OSCILLATION CRITERIA FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS”. Gazi University Journal of Science 29, no. 4 (December 2016): 923-27.
EndNote Mısır A, Öğrekçi S (December 1, 2016) OSCILLATION CRITERIA FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS. Gazi University Journal of Science 29 4 923–927.
IEEE A. Mısır and S. Öğrekçi, “OSCILLATION CRITERIA FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS”, Gazi University Journal of Science, vol. 29, no. 4, pp. 923–927, 2016.
ISNAD Mısır, Adil - Öğrekçi, Süleyman. “OSCILLATION CRITERIA FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS”. Gazi University Journal of Science 29/4 (December 2016), 923-927.
JAMA Mısır A, Öğrekçi S. OSCILLATION CRITERIA FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS. Gazi University Journal of Science. 2016;29:923–927.
MLA Mısır, Adil and Süleyman Öğrekçi. “OSCILLATION CRITERIA FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS”. Gazi University Journal of Science, vol. 29, no. 4, 2016, pp. 923-7.
Vancouver Mısır A, Öğrekçi S. OSCILLATION CRITERIA FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS. Gazi University Journal of Science. 2016;29(4):923-7.