Journal of Nonlinear Mathematical Physics

Volume 17, Issue 4, December 2010, Pages 503 - 516

Nonlinear Stability Analysis of the Emden–Fowler Equation

Authors
C. G. Böhmer
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom,c.boehmer@ucl.ac.uk
T. Harko
Department of Physics and Center for Theoretical and Computational Physics, The University of Hong Kong, Pok Fu Lam Road, Hong Kong, Hong Kong SAR, P. R. China,harko@hkucc.hku.hk
Received 10 December 2009, Accepted 14 April 2010, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S1402925110001100How to use a DOI?
Keywords
Emden–Fowler equation; KCC-theory; stability
Abstract

In this paper, we qualitatively study radial solutions of the semilinear elliptic equation Δu+un = 0 with u(0) = 1 and u′(0) = 0 on the positive real line, called the Emden–Fowler or Lane–Emden equation. This equation is of great importance in Newtonian astrophysics and the constant n is called the polytropic index.

By introducing a set of new variables, the Emden–Fowler equation can be written as an autonomous system of two ordinary differential equations which can be analyzed using linear and nonlinear stability analysis. We perform the study of stability by using linear stability analysis, the Jacobi stability analysis (Kosambi–Cartan–Chern-theory) and the Lyapunov function method. Depending on the values of n these different methods yield different results. We identify a parameter range for n where all three methods imply stability.

Copyright
© 2010 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
17 - 4
Pages
503 - 516
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925110001100How to use a DOI?
Copyright
© 2010 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - C. G. Böhmer
AU  - T. Harko
PY  - 2021
DA  - 2021/01/07
TI  - Nonlinear Stability Analysis of the Emden–Fowler Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 503
EP  - 516
VL  - 17
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925110001100
DO  - https://doi.org/10.1142/S1402925110001100
ID  - Böhmer2021
ER  -