On a generalization of the Nicoletti problem for functional differential equations with advancing argument
type: Item
instance of: scholarly article
title: On a generalization of the Nicoletti problem for functional differential equations with advancing argument
zbMATH Open document ID: 0404.34053
DOI: 10.1007/BF01534247
author: K. Appert
published in: Monatshefte für Mathematik
publication date: 1979-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/177943
review text: Let \(B\) be a Banach space and \(\Phi\) the linear space of all continuous functions \(\varphi: [0,+\infty)\to B\). We consider the functional differential equation \[ \varphi'(t)=F(t,\varphi)\quad\text{for}\;t\in [0,+\infty)\tag{1} \] together with a generalized Nicoletti condition (2) \(H(\varphi)=\eta\). The function \(F: [0,+\infty)\times\Phi\to B\), \(H:\Phi \to B\) is a linear operator and \(\eta\in B\). Assume that (1) is an equation with unbounded advancement of argument, i.e. that the value of \(F(t,\varphi)\) may depend on the values of \(\varphi(t)\) for \(t\in[0,+\infty)\). Under suitable assumptions we show that when the solution satisfies a certain growth condition, then there exists exactly one solution of the problem (1), (2).
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 3627584
zbMATH Keywords: Nicoletti problem
zbMATH Keywords: functional differential equation with advancing argument
MaRDI profile type: Publication
cites work: Über die Nicoletti-Aufgabe für Funktional-Differentialgleichungen mit voreilendem Argument
cites work: Über Funktional-Differentialgleichungen mit voreilendem Argument
cites work: On Nested Functional Differential Equations
OpenAlex ID: W2319597620
description: scientific article; zbMATH DE number 3627584