Skip to main content
SpringerLink
Log in

Nonlinear oscillators with real valued powers: an analytic treatment

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

We give an analytic treatment of a second order ordinary differential equation describing a nonlinear oscillatory process with real valued power. This equation occurs in studying flows through porous media, heat conduction or plasma physics. After giving suitable conditions for the solubility of this equation in closed form, we tackle the related first boundary value problem and apply our analytic method to solve it. In the numerical section we discuss some models with fractional powers.

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. Ash RB (1971) Complex variables. Academic Press, New York, London

    MATH  Google Scholar 

  2. Citterio M, Talamo R (2009) The elliptic core of nonlinear oscillators. Meccanica 44(6):653–660

    Article  MathSciNet  MATH  Google Scholar 

  3. Gilding BH (1987) The first boundary value problem for \(-u^{\prime \prime }=\lambda u^p\). J Math Anal Appl 128(2):419–442

    Article  MathSciNet  MATH  Google Scholar 

  4. Peletier LA (1981) The porous media equation. In Applications of Nonlinear Analysis in the Physical Sciences (Bielefeld, 1979), volume 6 of Surveys Reference Works Math., pp. 229–241. Pitman, Boston, Mass.-London

  5. Rakaric Z (2011) Oscillators with a quasi-constant restoring force: approximations for motion. Meccanica 46(5):1047–1053

    Article  MATH  Google Scholar 

  6. Mingari Scarpello G, Ritelli D (2012) Closed form integration of a hyperelliptic, odd powers, undamped oscillator. Meccanica 47(4):857–862

  7. Temme NM (1996) Special functions. A Wiley-Interscience Publication. Wiley, New York. An introduction to the classical functions of mathematical physics

  8. Wong JSW (1975) On the generalized Emden–Fowler equation. SIAM Rev 17:339–360

    Article  MathSciNet  MATH  Google Scholar 

  9. Yildirim A (2010) Determination of periodic solutions for nonlinear oscillators with fractional powers by He’s modified Lindstedt-Poincaré method. Meccanica 45(1):1–6

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Politecnico di Milano, Via Bonardi, 9, 20133, Milan, Italy

    Maurizio Citterio & Rodolfo Talamo

Authors
  1. Maurizio Citterio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rodolfo Talamo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rodolfo Talamo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Citterio, M., Talamo, R. Nonlinear oscillators with real valued powers: an analytic treatment. Meccanica 52, 1257–1264 (2017). https://doi.org/10.1007/s11012-016-0474-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-016-0474-3

Keywords

Search

Navigation