Maximal regular boundary value problems in Banach-valued function spaces and applications
type: Item
instance of: scholarly article
title: Maximal regular boundary value problems in Banach-valued function spaces and applications
zbMATH Open document ID: 1128.46029
DOI: 10.1155/IJMMS/2006/92134
author: Veli B. Shakhmurov
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2007-06-13T00:00:00Z
full work available at URL: https://eudml.org/doc/53665
review text: The paper is devoted to the investigation of nonlocal boundary value problems for differential operator equations of second order in Banach-valued function spaces. It is assumed that the principal parts of the differential operators generated by these problems are non-selfadjoint. The author considers nonhomogeneous boundary value problems for ordinary differential operator equations, partial differential operator equations with dependent coefficients in the principal part, and nonlocal initial boundary value problems for parabolic differential operator equations. He gives conditions for the maximal regularity, positivity and the Fredholmness of the problems in Banach-valued \(L_p\)-spaces. The results are applied to nonlocal boundary value problems for quasi-elliptic partial differential equations, to infinite systems of nonlocal boundary value problems for elliptic equations with variable coefficients, and to nonlocal initial boundary value problems for parabolic equations on cylindrical domains.
Mathematics Subject Classification ID: 46N20
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 5164020
zbMATH Keywords: nonlocal boundary value problems
zbMATH Keywords: differential operator equations
zbMATH Keywords: maximal regularity
zbMATH Keywords: positivity
zbMATH Keywords: Fredholmness
zbMATH Keywords: Banach-valued spaces
reviewed by: Jiří Rákosník
MaRDI profile type: Publication
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OpenAlex ID: W1973965278
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description: scientific article; zbMATH DE number 5164020