On a functional differential equation arising in the theory of the distribution of wealth
type: Item
instance of: scholarly article
title: On a functional differential equation arising in the theory of the distribution of wealth
zbMATH Open document ID: 0567.35013
DOI: 10.1007/BF02189410
author: Wolfgang Eichhorn
author: Winfried Gleißner
published in: Aequationes Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137057
review text: The paper under review deals with the functional differential equation \((i)\quad p_ t(x,t)+(\beta +n\gamma)p(x,t)+\beta xp_ x(x,t)=\gamma n^ 2p(nx,t),\) \(x,t\in (0,+\infty)\), arising in the theory of the distribution of wealth. The author studies properties of solutions of (i) of the type \(p(x,t)=p(t)x^{-c},\) where \(c>1\), and multiplicative solutions \(\psi (x,t)=u(x)v(t)\). The proof uses an explicit expression of solutions of an initial problem for (i).
Mathematics Subject Classification ID: 35F10
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 91B62
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 3905057
zbMATH Keywords: functional differential equation
zbMATH Keywords: distribution of wealth
zbMATH Keywords: multiplicative solutions
Wikidata QID: Q115392727
reviewed by: Z. Kamont
MaRDI profile type: Publication
cites work: Theory of functional differential equations. 2nd ed
cites work: The Distribution of Wealth
cites work: On Stochastic Models of Size Distributions
cites work: Über ein modell zur paretoverteilung
cites work: A Model Explaining the Pareto Distribution of Wealth
description: scientific article; zbMATH DE number 3905057