On random solutions of Volterra-Fredholm integral equations
type: Item
instance of: scholarly article
title: On random solutions of Volterra-Fredholm integral equations
zbMATH Open document ID: 0534.60055
author: V. Sree Hari Rao
published in: Pacific Journal of Mathematics
publication date: 1983-01-01T00:00:00Z
review text: Existence, uniqueness and boundedness theorems for solutions of the nonlinear stochastic integral equation \[ x(t;\omega)=f(t;\omega)+\int^{t}_{0}a(t,s;\omega)g(s,x(s;\omega))ds+\i nt^{\infty}_{0}b(t,s;\omega)h(s,x(s;\omega))ds,\quad t\geq 0 \] are obtained using the admissibility theory of integral operators and contractor theory. Two additional boundedness results are proved in case g(t,x) and h(t,x) are independent of t and these results are illustrated by examples where \(b(t,s;\omega)\equiv 0\) and \(a(t,s;\omega)=a(t- s;\omega).\)
Mathematics Subject Classification ID: 60H20
zbMATH DE Number: 3848345
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: boundedness
zbMATH Keywords: admissibility
zbMATH Keywords: contractor
MaRDI profile type: Publication
full work available at URL: pjm.1983.108.397
OpenAlex ID: W2080781121
DOI: 10.2140/PJM.1983.108.397
description: scientific article; zbMATH DE number 3848345