Skip to main content
Log in

On solutions of Emden-Fowler-type equations

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

The paper deals with solutions to Emden-Fowler-type equations of any arbitrary order. The asymptotic properties of solutions to these equations are studied, and a systematic survey of numerous uncoordinated results of analysis of continuable and noncontinuable solutions is given.

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. R. Bellman, Stability Theory of Differential Equations (New York, 1953; Inostr. Lit., Moscow, 1954).

    Google Scholar 

  2. V. A. Kondrat’ev and V. S. Samovol, “On some asymptotic properties of solutions of Emden-Fowler-type equations,” Differ.Uravn. 17(4), 749–750 (1981).

    Google Scholar 

  3. I. T. Kiguradze and T. F. Chanturiya, Asymptotic Properties of Solutions to Nonautonomous Ordinary Differential Equations (Nauka, Moscow, 1990) [in Russian].

    Google Scholar 

  4. I. T. Kiguradze, “On the oscillatory character of solutions of the equation \(\tfrac{{d^m u}} {{dt^m }} + a(t)\left| u \right|^n\) sign u = 0,” Mat. Sb. 65(2), 172–187 (1964).

    MathSciNet  Google Scholar 

  5. I. V. Astashova, Qualitative Properties of Solutions to Differential Equations and Related Problems of Spectral Analysis (YuNITI-DANA, Moscow, 2012) [in Russian].

    Google Scholar 

  6. A. D. Bryuno, Power Geometry in Algebraic and Differential Equations (Nauka, Moscow, 1998) [in Russian].

    MATH  Google Scholar 

  7. A. D. Bryuno, “Asymptotic behavior and expansions of solutions of an ordinary differential equation,” Uspekhi Mat. Nauk [Russian Math. Surveys] 59(3), 31–80 (2004) [Russian Math. Surveys 59 (3), 429–480 (2004)].

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. S. Samovol.

Additional information

Original Russian Text © V. S. Samovol, 2014, published in Matematicheskie Zametki, 2014, Vol. 95, No. 5, pp. 775–789.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Samovol, V.S. On solutions of Emden-Fowler-type equations. Math Notes 95, 708–720 (2014). https://doi.org/10.1134/S0001434614050137

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434614050137

Keywords

Navigation