Skip to main content
Log in

On the uniform boundedness of solutions of some non-autonomous differential equations of the fourth order

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In this paper, sufficient conditions are established under which all solutions of some non-autonomous differential equations of the fourth order are bounded and uniformly bounded.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Reissig R, Sansone G, Conti R.Nonlinear Differential Equations of Higher Order [M]. Noordhoff International Publishing, 1974.

  2. Abou-El-Ela A M A, Sadek A I. On the asymptotic behaviour of solutions of some differential equations of the fourth order [J].Ann Differential Equations, 1992,8(1):1–12.

    MATH  MathSciNet  Google Scholar 

  3. Hara T. On the asymptotic behavior of the solutions of some third and fourth order non-autonomous differential equations [J].Publ Res Inst Math Sci, 1974,9:649–673.

    MATH  MathSciNet  Google Scholar 

  4. Jin Jun. On the uniform boundedness of the solution of the non-linear differential equation of the fourth order [J].Ann Differential Equations, 1988,4(2):159–171.

    MathSciNet  Google Scholar 

  5. Tunç C. On the asymptotic behaviour of solutions of some differential equations of the fourth order [J].Studia Univ Babes-Bolyai Math, 1994,39(2):87–96.

    MATH  MathSciNet  Google Scholar 

  6. Lasalle J, Lefschetz S.Stability by Liapunov’s Direct Method with Applications [M]. New York: Academic Press, 1961.

    Google Scholar 

  7. Yoshizawa T. Stability theory by Liapunov’s second method [Z]. The Mathematical Society of Japan, 1966.

  8. Ezeilo J O C. On the boundedness and the stability of solutions of some differential equations of the fourth order [J].J Math Anal Appl, 1962,5:136–146.

    Article  MATH  MathSciNet  Google Scholar 

  9. Lu Tinghe, Shen Jiaqi, Jin Jun. Construction and applications of Liapunov’s functions for differential equations of fourth order [J].Journal of Shanghai Teachers University, 1982,11(2). (in Chinese)

  10. Qin Yuanxun, Wang Lian Wang Muqiu.Theory and Application of Motion Stability [M]: Beijing: Science Press, 1981. (in Chinese)

    Google Scholar 

  11. Shen Jiaqi, Lu Tinghe, Jin Jun. The construction of Liapunov’s function of certain fourth order differential equations [J].Journal of Shanghai Teachers University, 1983,12(2). (in Chinese)

  12. Yoshizawa T. Liapunov’s function and boundedness of solution [J].Funkciaiaj Ekvacioj, 1959,2.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by Chien Weizang

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tunç, C. On the uniform boundedness of solutions of some non-autonomous differential equations of the fourth order. Appl Math Mech 20, 622–628 (1999). https://doi.org/10.1007/BF02464934

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02464934

Key words

CLC number

Navigation