Second order integro-differential equations of Volterra type on unbounded domains in Banach spaces
type: Item
instance of: scholarly article
title: Second order integro-differential equations of Volterra type on unbounded domains in Banach spaces
zbMATH Open document ID: 0959.45006
DOI: 10.1016/S0362-546X(98)00289-2
author: Dajun Guo
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2000-06-21T00:00:00Z
review text: The author investigates the initial value problem for second-order integro-differential equations of Volterra type \[ u''= f(t,u,u', Tu),\quad t\in J, \] \[ u(0)= u_0,\quad u'(0)= u_1, \] where \(J= [0,+\infty)\), \((u_0, u_1)\in E\times E\), \(E\) being a real Banach space, \(f\in C\) \((J\times E\times E\times E,E)\) and \[ (Tu)(t)= \int^t_0 K(t,s) u(s) ds,\quad t\in J, \] \(K\in C(D, \mathbb{R}_+)\), \(D= \{(t,s)\in J\times J; s\leq t\}\), \(\mathbb{R}_+= \{t\in \mathbb{R}; t\geq 0\}\). For this purpose, the author establishes a comparison result and uses the upper and lower solutions.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 1462157
zbMATH Keywords: initial value problem
zbMATH Keywords: second-order integro-differential equations of Volterra type
zbMATH Keywords: Banach space
zbMATH Keywords: comparison result
zbMATH Keywords: upper and lower solutions
reviewed by: Dan-Mircea Borş
MaRDI profile type: Publication
full work available at URL: s0362-546x(98)00289-2
OpenAlex ID: W1987841718
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description: scientific article; zbMATH DE number 1462157