Skip to main content
SpringerLink
Log in

Nonlinear oscillations of fourth order quasilinear ordinary differential equations

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We consider fourth order quasilinear ordinary differential equations. Firstly, we classify positive solutions into four types according to their asymptotic properties. Then we derive existence theorems of positive solutions belonging to each type. Using these results, we can obtain an oscillation criterion, which is our main objective. Moreover, applying such criteria for ordinary differential equations to binary elliptic systems, we establish nonexistence theorems for positive solutions.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. Kamo and H. Usami, Oscillation theorems for fourth-order quasilinear ordinary differential equations, Studia Sci. Math. Hungar., 39 (2002), 385–406.

    MATH  MathSciNet  Google Scholar 

  2. T. Kusano and M. Naito, Nonlinear oscillation of fourth order differential equations, Can. J. Math., 28 (1976), 840–852.

    Article  MATH  MathSciNet  Google Scholar 

  3. T. Kusano and T. Tanigawa, On the structure of positive solutions of a class of fourth order nonlinear differential equations, Annali di Mathematica, 185 (2006), 521–536.

    Article  MathSciNet  Google Scholar 

  4. T. Kusano and M. Naito, On fourth-order nonlinear oscillations, J. London Math. Soc., 14 (1976), 91–105.

    Article  MATH  MathSciNet  Google Scholar 

  5. M. Naito and F. Wu, A note on the existence and asymptotic behavior of nonoscillatory solutions of fourth order quasilinear differential equations, Acta Math. Hungar., 102 (2004), 177–202.

    Article  MATH  MathSciNet  Google Scholar 

  6. D. R. Smart, Fixed Point Theorems, Cambridge University Press (London, 1974).

    MATH  Google Scholar 

  7. T. Tanigawa, Oscillation and nonoscillation theorems for a class of fourth order quasilinear functional differential equations, Hiroshima Math. J., 33 (2003), 297–316.

    MATH  MathSciNet  Google Scholar 

  8. F. Wu, Nonoscillatory solutions of fourth order quasilinear differential equations, Funkcial. Ekvac., 45 (2002), 71–88.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Liberal Arts and Sciences, Sapporo Medical University, S1 W16, Chuo-ku, Sapporo, Hokkaido, Japan, 060-8556

    Ken-ichi Kamo

  2. Department of Mathematical and Design Engineering, Faculty of Engineering, Gifu University, 1-1 Yanagido, Gifu, Japan, 501-1193

    Hiroyuki Usami

Authors
  1. Ken-ichi Kamo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hiroyuki Usami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ken-ichi Kamo.

Additional information

Corresponding author.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kamo, Ki., Usami, H. Nonlinear oscillations of fourth order quasilinear ordinary differential equations. Acta Math Hung 132, 207–222 (2011). https://doi.org/10.1007/s10474-011-0127-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-011-0127-x

Keywords

2000 Mathematics Subject Classification

Search

Navigation