Oscillations of Solutions for Nonlinear Differential Equations

المؤلفون

  • Jaffalah J. Amhalhil Sirte University, School of Mathematical Sciences, Faculty of Education

الكلمات المفتاحية:

Oscillation criteria، ordinary differential equations، Second order، Nonlinear

الملخص

It is know that many problems in physics, in the study of chemically reacting systems, in celestial mechanics and in other fields of science can be modelled by second order nonlinear differential equations. Therefore, the asymptotic and oscillatory properties of solutions of such equations have been investigated by many authors. In this paper our aim is to present some new sufficient conditions for the oscillation of all solutions of the nonlinear differential equations of the form

(r(t)y (x(t))x(t)) + g1 (t, x(t)) = 0

Our new results extend and improve a number of existing oscillation criteria. Further, Our main results are illustrated with examples.

المراجع

F. V. Atkinson, On second order nonlinear oscillations. Pacific. J. Math. 5(1955), P.643-647.

E. M.Elabbasy and Sh. R. Elzeiny, Oscillation theorem concerning non-linear differential equations of the second order, Opu. Math. 31 (2011), P. 373-391.

M. M. A. El-Sheikh, Oscillation and non-oscillation criteria for second order nonlinear differential equations I , J. Math. Anal. Appl. 179 (1993) , p. 14-27.

S. R. Grace, Oscillation theorems for second order nonlinear differential equations with damping, Math, Nachr. 141 (1989), p. 117-127.

S. R. Grace, Oscillation theorems for nonlinear differential equations ofsecond order, J. Math. Anal. Appl. 171 (1992), p. 220 − 241.

S. R. Grace and B. S. Lalli, Oscillation theorems for nonlinear second order functional differential equations with damping, Bull. Inst. Math. Acad. Sinica 13 (1985), p. 183-192.

J. R. Graef and P. W. Spikes, On the oscillatory behaviour of solutions of second order nonlinear differential equations. Czech. Math. J. 36 (1986), p. 275-284.

P. Hartman, Non-oscillatory linear differential equation of second order, Amer. J. Math. 74 (1952), p. 389 – 400.

I. V. Kamenev, Integral criterion for oscillation of linear differential equations of second order, Math. Zametki 23 (1978), p. 249 - 251.

J. V. Manojlovic, Oscillation criteria for second order sub linear differential equation, Comput. Math. Appl. 39 (2000), p. 161-172.

J. V. Manojlovic, Integral averages and oscillation of second order nonlinear differential equations, Comput. Math. Appl. 41 (2001), p. 1521-1534.

J. Ohriska and A. Zulova , Oscillation criteria for second order nonlinear differential equations, Im preprint series A, No.10(2004), p.1-11.

CH. G. Philos, A second order super linear oscillation criterion, Canad. Math. Bull. 27 (1984)

, p. 102-112.

A. Tiryaki and A. Zafer, Oscillation criteria for second order nonlinear differential equations with damping, Turk. J. Math. 24 (2000), p.185 - 196.

A. Wintner, A criterion of oscillatory stability, Quart, Appl. Math. 7 (1949), p. 115 -117.

J. S. W. Wong, Oscillation theorems for second order nonlinear differential equations, Bull. Inst. Math. Sinica 3 (1975), p. 283-309.

التنزيلات

منشور

2023-01-26