On the solvability of boundary value problems for an abstract Bessel-Struve equation
type: Item
instance of: scholarly article
title: On the solvability of boundary value problems for an abstract Bessel-Struve equation
zbMATH Open document ID: 1451.34082
DOI: 10.1134/S001226611908007X
author: A. V. Glushak
published in: Differential Equations
publication date: 2019-12-03T00:00:00Z
review text: The paper deals with the abstract Bessel-Struve equation \[u''(t) + kt^{-1}\left(u'(t)-u'(0)\right) = A u(t), t>0,\] where \(A\) is a densely defined closed linear operator on a complex Banach space \(E\) and \(k>0\). Dirichlet and Neumann boundary value problems associated with this equations are considered, that are both not well-posed in general. Following the results from [\textit{A. V. Glushak}, Differ. Equ. 53, No. 7, 864--878 (2017; Zbl 1382.34065)] the author assumes that \(A\) is contained in the set of generators of integrated cosine operator functions and establishes further sufficient conditions on \(A\) and the boundary values for the unique solvability of both problems.
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47D62
zbMATH DE Number: 7139202
zbMATH Keywords: Bessel-Struve equation
zbMATH Keywords: boundary value problem
zbMATH Keywords: classical solution
zbMATH Keywords: integrated cosine operator functions
zbMATH Keywords: Bessel and Struve operator functions
reviewed by: Marjeta Kramar Fijavž
Wikidata QID: Q115250538
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7139202