Abstract
The existence of slowly and regularly varying solutions in the sense of Karamata implying nonoscillation is proved for a class of second order nonlinear retarded functional differential equations of Thomas-Fermi type. A motivation for such study is the extensively developed theory offering a number of properties of regularly and slowly varying functions ([2]) - consequently of such solutions of differential equations. As an illustration, the precise asymptotic behaviour for $t\rightarrow \infty$ of the slowly varying solutions for a subclass of considered equations is presented.
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