An inverse problem for a second-order differential equation in a Banach space
type: Item
instance of: scholarly article
title: An inverse problem for a second-order differential equation in a Banach space
zbMATH Open document ID: 1078.34036
DOI: 10.1155/S108533750440308X
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2005-04-29T00:00:00Z
full work available at URL: https://eudml.org/doc/51926
review text: The author considers in a Banach space \(E\) the differential equation \[ d^2v / dt^2 = Av + f(t) + p, \] with \(0 \leq t \leq t_1\). Here, \(A\) is a linear unbounded operator generating a cosine operator function, \(f\) is continuous on \([0, t_1]\) with values in \(E\), and \(p\) is an unknown element of \(E\). The boundary conditions \[ v(0) = v_0, \quad v'(0) = v'_0, \quad\text{and} \quad v(t_1) = v_1, \] are given. The problem considered here is to find a pair \((v(t), p)\) satisfying the equation (in the classical sense) and the boundary conditions. The author obtains necessary and sufficient conditions for the unique solvability of this problem.
reviewed by: Vassilis G. Papanicolaou
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 34A55
zbMATH DE Number: 2163693
zbMATH Keywords: linear unbounded operator generating a cosine operator function
zbMATH Keywords: differential equation in a Banach space
Wikidata QID: Q115243257
MaRDI profile type: Publication
OpenAlex ID: W2034495375
description: scientific article; zbMATH DE number 2163693