OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS

Abstract

In this paper, we are concerned with the oscillations in forced second order nonlinear differential equations with nonlinear damping terms. By using clasical variational principle and averaging technique, new oscillation criteria are established, which improve and extend some recent results. Examples are also given to illustrate the results.

References

1. M.S. Keener, Solutions of a certain linear
2. nonhomogeneous second order differential
3. equations, Appl. Anal. 1 (1971) 57–63.
4. A.Skidmore, W. Leighton, On the
5. equation y '' p  x y  f  x J. Math. Anal.
6. Appl. 43 (1973) 46–55.
7. A. Skidmore, J. J. Bowers, Oscillation behavior of
8. y '' p  x y  f  x , J. Math. Anal. Appl. 49

9. (1975) 317–323.
10. S.M. Rainkin, Oscillation theorems for second
11. order nonhomogeneous linear differential
12. equations, J. Math. Anal. Appl. 53 (1976) 550–553.
13. J.S.W. Wong, Second order nonlinear forced
14. oscillations, SIAM J. Math. Anal. 19 (1988) 667–
15. F. Jiang, F. Meng, New oscillation criteria for a
16. class of second-order nonlinear forced differential
17. equations, J. Math. Anal. Appl. 336 (2007) 1476–
18. S.P. Rogovchenko, Y.V. Rogovchenko, Oscillation
19. theorems for differential equation with a nonlinear
20. damping term, J. Math. Anal. Appl. 279 (2003)
21. –134.
22. A. Tiryaki, A. Zafer, Interval oscillation of a
23. general class of second-order nonlinear differential
24. equations with nonlinear damping, Nonlinear Anal.
25. (2005) 49–63.
26. A. Tiryaki, A. Zafer, Oscillation of Second-Order
27. Nonlinear Different ial Equations with Nonlinear
28. Damping, Mathematical and Computer modelling
29. (2004) 197-208.
30. X. Zhao, F. Meng, Oscillation of second-order
31. nonlinear ODE with damping, Appl. Math.Comput.
32. (2006) 1861–1871.
33. Y. Huang, F. Meng, Oscillation of second-order
34. nonlinear ODE with damping, Appl. Math.
35. Comput. 199 (2008) 644–652.
36. A. Zhao, Y. Wang, J. Yan, Oscillation criteria for
37. second-order nonlinear differential equations with
38. nonlinear damping, Computers and Mathematics
39. with Applications 56 (2008) 542–555.
40. F. Meng, Y. Huang, Interval oscillation criteria for
41. a forced second-order nonlinear differential
42. equations with damping, Appl. Math.Comput. 218
43. (2011) 1857–1861.
44. W. Shi, Interval oscillation criteria for a forced
45. second-order differential equation with nonlinear
46. damping, Mathematical and Computer modelling
47. (2006) 170–177.
48. G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities,
49. second ed., Cambridge University Press,
50. Cambridge, 1988.