Positive solutions of nonlinear integral equations arising in infectious diseases
type: Item
instance of: scholarly article
title: Positive solutions of nonlinear integral equations arising in infectious diseases
zbMATH Open document ID: 0658.45012
DOI: 10.1016/0022-247X(88)90002-9
author: Dajun Guo
author: V. Lakshmikantham
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: The following nonlinear integral equation (1) \(x(t)=\int^{t}_{t- \tau}f(s,x(s))ds\) can be interpreted as a model for the spread of certain infectious diseases. This equation is examined in the heading under the assumptions that f(t,x) is nonnegative and continuous on the set \(R\times R_+\), is \(\omega\)-periodic in t and such that \(f(t,0)=0\) for \(t\in R\). Under some additional assumptions the equation (1) is proved to have at least two nontrivial, nonnegative, continuous and \(\omega\)-periodic solutions. A result on the convergence of the sequence of successive approximations is also established. A few examples illustrate the applicability of results obtained in this interesting paper.
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 4075790
zbMATH Keywords: infectious diseases
zbMATH Keywords: periodic solutions
zbMATH Keywords: convergence
zbMATH Keywords: successive approximations
reviewed by: Józef Banaś
MaRDI profile type: Publication
cites work: A fixed point theorem with application to an infectious disease model
cites work: Nonzero Solutions of Nonlinear Integral Equations Modeling Infectious Disease
cites work: Q3994493
description: scientific article; zbMATH DE number 4075790