Local existence of some nonlinear Volterra integrodifferential equations with infinite delay
type: Item
instance of: scholarly article
title: Local existence of some nonlinear Volterra integrodifferential equations with infinite delay
zbMATH Open document ID: 1207.34095
author: Jung-Chan Chang
author: Chun-Liang Shih
author: Chien-Ning Yeh
author: Cheng Lien Lang
published in: Taiwanese Journal of Mathematics
publication date: 2010-05-14T00:00:00Z
review text: The authors prove local existence and uniqueness of solutions to the Volterra integrodifferential equation \[ \begin{cases} u'(t) = Au(t)+\int_0^tk(t,\theta ,u(\theta))\,d\theta +F(t,u_t), & 0\leq t\leq T, \\ u_0 = \varphi \in \mathcal{P}.\end{cases} \] Here, \(A:D(A)\to X\) is a nondensely defined Hille-Yosida operator, the phase space \(\mathcal{P}\) is an abstract admissible linear space of functions mapping \((-\infty ,0]\) into \(X\) and \(u_t\in \mathcal{P}\). Some properties of the solutions are also given.
reviewed by: A. Rhandi
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5707735
zbMATH Keywords: equations in abstract spaces
zbMATH Keywords: infinite delay
zbMATH Keywords: Volterra integrodifferential equations
zbMATH Keywords: nonlinear equations
zbMATH Keywords: Hille-Yosida operators
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500405732
OpenAlex ID: W4235513128
DOI: 10.11650/TWJM/1500405732
description: scientific article; zbMATH DE number 5707735