期刊
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
卷 17, 期 4, 页码 503-516出版社
TAYLOR & FRANCIS LTD
DOI: 10.1142/S1402925110001100
关键词
Emden-Fowler equation; KCC-theory; stability
资金
- government of the Hong Kong SAR
In this paper, we qualitatively study radial solutions of the semilinear elliptic equation Delta u+u(n) = 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.
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