## Hiroshima Mathematical Journal

### Regularly Varying Solutions of Second Order Nonlinear Functional Differential Equations with Retarded Argument

#### 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.

#### Article information

Source
Hiroshima Math. J., Volume 41, Number 2 (2011), 137-152.

Dates
First available in Project Euclid: 24 August 2011

https://projecteuclid.org/euclid.hmj/1314204558

Digital Object Identifier
doi:10.32917/hmj/1314204558

Mathematical Reviews number (MathSciNet)
MR2849151

Zentralblatt MATH identifier
1240.34371

#### Citation

Takaŝi, Kusano; Marić, V. Regularly Varying Solutions of Second Order Nonlinear Functional Differential Equations with Retarded Argument. Hiroshima Math. J. 41 (2011), no. 2, 137--152. doi:10.32917/hmj/1314204558. https://projecteuclid.org/euclid.hmj/1314204558

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