Skip to main content
SpringerLink
Log in

On the Singularities of the Emden–Fowler Type Equations

  • Conference paper
Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

Abstract

We study the Emden–Fowler type equations and their analytic solutions at the origin. We explain the structure of movable singularities of these solutions and visualize them numerically.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. A. Aslanov, Determination of convergence intervals of the series solutions of Emden–Fowler equations using polytropes and isothermal spheres. Phys. Lett. A 372, 3555–3561 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. R. Bellman, Stability Theory of Differential Equations (Dover, New York, 2008)

    Google Scholar 

  3. P. Breitenlohner, P. Forgács, D. Maison, Static spherically symmetric solutions of the Einstein–Yang–Mills equations. Commun. Math. Phys. 163, 141–172 (1994)

    Article  MATH  Google Scholar 

  4. O. Costin, M. Huang, Behavior of lacunary series at the natural boundary. Adv. Math. 222(4), 1370–1404 (2009). Commun. Math. Phys. 163, 141–172 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. H.T. Davis, Introduction to Nonlinear Differential and Integral Equations (Dover, New York, 2010)

    Google Scholar 

  6. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series and Products (Academic Press, San Diego, 1994)

    MATH  Google Scholar 

  7. E. Hille, Ordinary Differential Equations in the Complex Domain (Dover, New York, 1997)

    MATH  Google Scholar 

  8. C. Hunter, Series solutions for polytropes and the isothermal sphere. Mon. Not. R. Astron. Soc. 328, 839–847 (2001)

    Article  Google Scholar 

  9. E.L. Ince, Ordinary Differential Equations (Dover, New York, 1956)

    Google Scholar 

Download references

Acknowledgements

RK is supported by the Warsaw Center of Mathematics and Computer Science from the funds of the Polish Leading National Research Centre (KNOW). GF is supported by NCN grant 2011/03/B/ST1/00330. RK is also grateful to Rod Halburd and Thomas Kecker (UCL, UK) for illuminating discussions.

Author information

Authors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Radosław Antoni Kycia & Galina Filipuk

Authors
  1. Radosław Antoni Kycia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Galina Filipuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Radosław Antoni Kycia .

Editor information

Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, Kraków, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Kycia, R.A., Filipuk, G. (2015). On the Singularities of the Emden–Fowler Type Equations. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_13

Download citation

Publish with us

Policies and ethics

Search

Navigation