## Hiroshima Mathematical Journal

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

### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.32917/hmj/1314204558

**Mathematical Reviews number (MathSciNet)**

MR2849151

**Zentralblatt MATH identifier**

1240.34371

**Subjects**

Primary: 34K06: Linear functional-differential equations 26A12: Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48]

**Keywords**

Functional differential equations retarded argument slowly, regularly varying functions Karamata Thomas-Fermi model Schauder-Tychonoff fixed point theorem

#### 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