An asymptotic analysis of positive solutions of generalized Thomas–Fermi differential equations — The sub-half-linear case

The existence and the asymptotics behavior for the large value of the variable of the positive solutions of generalized Thomas–Fermi equation presented in this article are proved. It is assumed that coefficient q(t)q(t) belongs to the class of regularly varying functions in the sense of Karamata. Properties of these functions and the Schauder–Tychonoff fixed point theorem are the main tools for the proofs.