Nonlinear Stability Analysis of the Emden–Fowler Equation
- https://doi.org/10.1142/S1402925110001100How to use a DOI?
- Emden–Fowler equation; KCC-theory; stability
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.
- © 2010 The Authors. Published by Atlantis Press and Taylor & Francis
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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 -