Generalized Thomas-Fermi Equations as the Lampariello Class of Emden-Fowler Equations
Abstract
The study examines a family of Emden-Fowler equations via Lampariello's parameter, proves non-integrability through Abel equation invariants, and performs phase-plane analysis of the associated dynamical system.
A one-parameter family of Emden-Fowler equations defined by Lampariello's parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p=1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.
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