Regularly varying solutions of second order nonlinear functional differential equations with retarded argument
type: Item
instance of: scholarly article
title: Regularly varying solutions of second order nonlinear functional differential equations with retarded argument
zbMATH Open document ID: 1240.34371
author: Kusano Takaŝi
author: Vojislav Marić
published in: Hiroshima Mathematical Journal
publication date: 2011-10-11T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.hmj/1314204558
review text: 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.
reviewed by: Bolis Basit
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5956513
zbMATH Keywords: functional differential equations
zbMATH Keywords: retarded argument
zbMATH Keywords: slowly
zbMATH Keywords: regularly varying functions
zbMATH Keywords: Thomas-Fermi model
zbMATH Keywords: Schauder-Tychonoff fixed point theorem
MaRDI profile type: Publication
cites work: Q4726487
cites work: Q4692282
cites work: Remarks on the existence of regularly varying solutions for second order linear differential equations
cites work: On a class of functional differential equations having slowly varying solutions
cites work: Q3510386
cites work: Regular variation and differential equations
cites work: Existence and asymptotic behavior of proper solutions of a class of second-order nonlinear differential equations
OpenAlex ID: W1585102142
Wikidata QID: Q128899467
DOI: 10.32917/HMJ/1314204558
description: scientific article; zbMATH DE number 5956513