Regularly varying solutions of second order nonlinear functional differential equations with retarded argument
A measurable function \(L: [0,\infty) \to (0,\infty)\) is said to be slowly varying (SV) if it satisfies \(L(\lambda t)/L(t)\to 1 \) as \(t\to\infty\) for all \(\lambda >0\). The function \(f(t)= t^{\rho} L(t)\) is said to be regularly varying (\(RV(\rho)\)). In this paper, the authors prove the existence of slowly and regularly varying solutions in the sense of Karamata implying nonoscillation for a class of second order nonlinear retarded functional equations of Thomas-Fermi type. The precise asymptotic behaviour for \(t\to \infty\) of the slowly varying solutions for a subclass of the considered equations is presented.
scientific article; zbMATH DE number 5956513