Almost convergence of solutions of nonlinear Volterra equations in Banach space
type: Item
instance of: scholarly article
title: Almost convergence of solutions of nonlinear Volterra equations in Banach space
zbMATH Open document ID: 0595.35014
DOI: 10.1016/0022-0396(86)90097-5
author: Kazuo Kido
published in: Journal of Differential Equations
publication date: 1986-01-01T00:00:00Z
review text: The author studies the asymptotic behavior of a solution of a nonlinear Volterra integral equation in a real uniformly convex Banach space E. Let A be an m-accretive operator in \(E\times E\) and b [resp. f] be a locally absolutely continuous function from [0,\(\infty)\) into R [resp. E] such that \(b(0)>0\) [resp. f(0)\(\in \overline{D(A)}]\). Assume that u is a bounded solution of the following Volterra equation: \[ u(t)+\int^{t}_{0}b(t-s)A(u(s))ds\ni f(t),\quad t\geq 0. \] Under some additional conditions the weak convergence of (1/T)\(\int^{T}_{0}u(s)ds\) as \(T\to \infty\) is obtained. It is proved by applying directly a nonlinear ergodic theorem for contraction semigroups in Banach spaces.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 3957728
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: nonlinear Volterra integral equation
zbMATH Keywords: m-accretive operator
zbMATH Keywords: nonlinear ergodic theorem
zbMATH Keywords: contraction semigroups in Banach spaces
MaRDI profile type: Publication
full work available at URL: 0022-0396(86)90097-5
OpenAlex ID: W2094965279
cites work: Q4064547
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description: scientific article; zbMATH DE number 3957728