J. V. Manojlović and V. Marić

An Asymptotic Analysis of Positive Solutions of Thomas-Fermi Type Sublinear Differential Equations

abstract:
The set of positive solutions of Thomas--Fermi type differential equation $$ x'' =q(t)\phi (x) $$
is studied under the assumptions that $q$, $\phi$ are regularly varying functions in the sense of Karamata. It is shown that such solutions exist and their accurate asymptotic behavior at infinity is determined.

Mathematics Subject Classification: Primary 34A34; Secondary 26A12

Key words and phrases: Thomas-Fermi differential equation, sublinear case, existence, asymptotic behavior of solutions, positive solutions, regular variation