Qualitative Properties of the Solutions to the Lane–Emden Equation in the Cylindrical Setup

Arsen Palestini () and Simone Recchi
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Arsen Palestini: Dipartimento di Metodi e Modelli per l’Economia il Territorio e la Finanza MEMOTEF, Sapienza University of Rome, Via del Castro Laurenziano 9, 00161 Rome, Italy
Simone Recchi: Independent Researcher, Urbangasse 6/3/41, 1170 Wien, Austria

Mathematics, 2024, vol. 12, issue 4, 1-11

Abstract: We analyze the Lane–Emden equations in the cylindrical framework. Although the explicit forms of the solutions (which are also called polytropes) are not known, we identify some of their qualitative properties. In particular, possible critical points and zeros of the polytropes are investigated and discussed, leading to possible improvements in the approximation methods which are currently employed. The cases when the critical parameter is odd and even are separately analyzed. Furthermore, we propose a technique to evaluate the distance between a pair of polytropes in small intervals.

Keywords: Lane–Emden equation; polytrope; ODEs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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