  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.
