Hiroshima Mathematical Journal

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

Kusano Takaŝi and V. Marić

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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


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References

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