Boundary-value problems and Cauchy problems for the second-order Euler operator differential equation
type: Item
instance of: scholarly article
title: Boundary-value problems and Cauchy problems for the second-order Euler operator differential equation
zbMATH Open document ID: 0624.34014
DOI: 10.1016/0024-3795(87)90056-5
author: L. Jódar
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: This paper deals with some linear differential equations on an abstract space, precisely the space of bounded operators on a Hilbert space. The model equation is a second order Euler equation with operator coefficients together with several boundary value conditions. Looking for solutions of the initial value problem of the form exp (tX) an algebraic equation is derived for X. Assuming the existence of such a solution, the question of existence of solutions to the boundary value problems is expressed in terms of algebraic conditions involving X and the operator coefficients connected to the equation. Some interesting general results related to functional operator equations are employed here, with appropriate references.
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 4013055
zbMATH Keywords: space of bounded operators on a Hilbert space
zbMATH Keywords: second order Euler equation with operator coefficients
Wikidata QID: Q115364355
reviewed by: Ovide Arino
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90056-5
OpenAlex ID: W1976514517
cites work: Operators which are annihilated by analytic functions and invariant subspaces
cites work: Solving Linear Operator Equations
cites work: Q3939931
cites work: Q5592564
cites work: Q3957479
cites work: Solution of the Equation $AX + XB = C$ by Inversion of an $M \times M$ or $N \times N$ Matrix
cites work: Boundary value problems for second-order differential operator equations
cites work: Q5600360
cites work: Q5686535
cites work: On factorization of operator polynomials and analytic operator functions
cites work: Q4059478
cites work: Q4726901
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description: scientific article; zbMATH DE number 4013055