The boundary-value problem for differential-operator equations of the first order in a locally convex space
type: Item
instance of: scholarly article
title: The boundary-value problem for differential-operator equations of the first order in a locally convex space
zbMATH Open document ID: 1237.34109
DOI: 10.3103/S1066369X11020010
author: N. A. Aksyonov
published in: Russian Mathematics
publication date: 2011-11-18T00:00:00Z
review text: Let \(H\) be a countably complete locally convex space, with topology generated by a multi-norm \(\{\|\cdot\|_p: \enskip p\in{\mathcal{P}}\}\) and let \(A:H\to H\) be a linear continuous operator. The author investigates the problem of finding a solution of equation \[ u'(t)=Au(t) \] satisfying the boundary condition \[ \mu u(a)-u(b)=x_0, \] where \(u:\mathbb{C}\to H\) is a vector-valued function, \(a, b\in \mathbb{C}\), \(a\neq b,\) \(\mu\neq 0\) and \(x_0\) is a point in an appropriate domain depending on the operator \(A\).
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5975440
zbMATH Keywords: linear differential equations in abstract spaces
zbMATH Keywords: boundary value problems
reviewed by: George Karakostas
MaRDI profile type: Publication
cites work: Q3683061
cites work: Q3957340
cites work: Q5531981
cites work: Q3244654
cites work: On the order and type of an operator.
cites work: Analytic solutions to differential operator equations in locally convex spaces
cites work: Q3416337
full work available at URL: s1066369x11020010
OpenAlex ID: W2075941451
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description: scientific article; zbMATH DE number 5975440