On the theory of an integral equation
type: Item
instance of: scholarly article
title: On the theory of an integral equation
zbMATH Open document ID: 0808.45007
author: Emanuel Gluskin
published in: Advances in Applied Mathematics
publication date: 1995-03-16T00:00:00Z
review text: The main object of the study in the paper is the following integral equation (1) \(x(t) = f(t) - \mu \int^ \infty_ 0 K(\tau) \text{sign} [x(t - \tau)] d \tau\). Here it is assumed that \(\mu \geq 0\), \(f\) is a continuous function having only isolated zeros \(t_ k\) such that \(f'(t_ k) \neq 0\) for \(k=1,2, \dots\). Moreover, the kernel function \(K\) satisfies some assumptions expressed in terms of the possibility to be applied in the description of electrical circuits. The author considers many qualitative properties of the solution of the equation (1) which appear in the modern electrical and electronics industry and technology. For example, the oscillatory and periodicity character of solutions of (1) is studied in connection with the resistance, voltage and sensitivity of electrical circuits. In the reviewer's opinion the paper has rather purely applied character. It can be recommended to workers in electrical engineering.
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 45M15
Mathematics Subject Classification ID: 78A55
Mathematics Subject Classification ID: 00A06
zbMATH DE Number: 694992
zbMATH Keywords: oscillatory solution
zbMATH Keywords: periodic solution
zbMATH Keywords: electrical circuits
zbMATH Keywords: resistance
zbMATH Keywords: voltage
zbMATH Keywords: sensitivity
zbMATH Keywords: electrical engineering
reviewed by: Józef Banaś
MaRDI profile type: Publication
full work available at URL: aama.1994.1011
OpenAlex ID: W2027994132
DOI: 10.1006/AAMA.1994.1011
description: scientific article; zbMATH DE number 694992