OSCILLATION CRITERIA FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS

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

Adil Mısır , Süleyman Öğrekçi

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).