Asymptotic properties of solutions of time-dependent Volterra integral equations
type: Item
instance of: scholarly article
title: Asymptotic properties of solutions of time-dependent Volterra integral equations
zbMATH Open document ID: 0675.45015
DOI: 10.1016/0022-247X(88)90216-8
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: The author studies the asymptotic behavior as \(t\to \infty\) of solutions of the time-dependent nonlinear Volterra integral equation \[ (1)\quad u(t)+\int^{t}_{0}b(t-s)A(s)u(s)ds\ni f(t),\quad t\in R_+=[0,\infty). \] Here b: \(R_+\to R\) is a given kernel, A(t) is (for each \(t\geq 0)\) a maximal monotone, multivalued operator on a real Hilbert space H and f: \(R_+\to H\). The integral appearing in (1) is taken in the sense of Bochner. The results of the paper generalize a lot of ones concerning (1) when A does not depend on t.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 4105586
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: time-dependent nonlinear Volterra integral equation
zbMATH Keywords: maximal monotone, multivalued operator
zbMATH Keywords: Hilbert space
author: Sergiu Aizicovici
reviewed by: Józef Banaś
MaRDI profile type: Publication
cites work: Q4114316
cites work: On the asymptotic behaviour of solutions of volterra equations in Hilbert space
cites work: Q3712927
cites work: On multivalued evolution equations in Hilbert spaces
cites work: Ergodic theorems for non-linear Volterra equations in Hilbert space
cites work: Q5665783
cites work: Asymptotic Behavior of Solutions of Nonlinear Volterra Equations with Completely Positive Kernels
cites work: Q3940286
cites work: An abstract functional differential equation and a related nonlinear Volterra equation
cites work: Q4097611
cites work: Q3284078
cites work: Asymptotic behavior of solutions to a class of nonlinear evolution equations
cites work: On some integral and integro-differential equations in a Hilbert space
cites work: On a nonlinear Volterra integral equation in a Banach space
cites work: An Existence Result for a Nonlinear Volterra Integral Equation in a Hilbert Space
cites work: Asymptotic behavior of solutions of nonlinear Volterra equations
cites work: Asymptotic behavior of solutions to nonlinear Volterra integral equations
cites work: Q3811038
cites work: On the asymptotic behavior of solutions of evolution equations associated with nonlinear Volterra equations
cites work: Heat transfer between solids and gases under nonlinear boundary conditions
cites work: Asymptotic behavior of the solutions of a class of functional differential equations: remarks on a related Volterra equation
cites work: Q3916996
cites work: Remarks on nonlinear ergodic theory in Hilbert space
cites work: Some energy estimates for a nondifferentiated Volterra equation
description: scientific article; zbMATH DE number 4105586