Journals / Gazi University Journal of Science / 2016 / Volume: 29 Issue: 4

OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS

Pages
—
Publication Date
2016-12-19
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Examples are also given to illustrate the results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we are concerned with the oscillations in forced second order nonlinear differential equations with nonlinear damping terms.
📊
Key Findings & Data:By using clasical variational principle and averaging technique, new oscillation criteria are established, which improve and extend some recent results.
💡
Conclusion & Impact:Examples are also given to illustrate the results.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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.

🔖

Cite This Article

Mısır, A., Öğrekçi, S. (2016). OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS. Gazi University Journal of Science, Volume: 29 Issue: 4. https://ajindex.com/articles/1269461

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (49)

  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. 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. A. Tiryaki, A. Zafer, Interval oscillation of a
  22. general class of second-order nonlinear differential
  23. equations with nonlinear damping, Nonlinear Anal.
  24. 49–63.
  25. A. Tiryaki, A. Zafer, Oscillation of Second-Order
  26. Nonlinear Different ial Equations with Nonlinear
  27. Damping, Mathematical and Computer modelling
  28. X. Zhao, F. Meng, Oscillation of second-order
  29. nonlinear ODE with damping, Appl. Math.Comput.
  30. 1861–1871.
  31. Y. Huang, F. Meng, Oscillation of second-order
  32. nonlinear ODE with damping, Appl. Math.
  33. Comput. 199 (2008) 644–652.
  34. A. Zhao, Y. Wang, J. Yan, Oscillation criteria for
  35. second-order nonlinear differential equations with
  36. nonlinear damping, Computers and Mathematics
  37. with Applications 56 (2008) 542–555.
  38. F. Meng, Y. Huang, Interval oscillation criteria for
  39. a forced second-order nonlinear differential
  40. equations with damping, Appl. Math.Comput. 218
  41. 1857–1861.
  42. W. Shi, Interval oscillation criteria for a forced
  43. second-order differential equation with nonlinear
  44. damping, Mathematical and Computer modelling
  45. 170–177.
  46. G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities,
  47. second ed., Cambridge University Press,
  48. Cambridge, 1988.
  49. y '' p  x y  f  x, J. Math. Anal. Appl. 49