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 () - 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.
"Regularly Varying Solutions of Second Order Nonlinear Functional Differential Equations with Retarded Argument." Hiroshima Math. J. 41 (2) 137 - 152, 2011. https://doi.org/10.32917/hmj/1314204558