Differential equations with operator coefficients in Hilbert spaces
type: Item
instance of: scholarly article
title: Differential equations with operator coefficients in Hilbert spaces
zbMATH Open document ID: 0807.34073
DOI: 10.1007/BF01207725
author: G. I. Aslanov
published in: Mathematical Notes
publication date: 1994-07-13T00:00:00Z
review text: This article deals with the equation \(\sum_{|\alpha|\leq m} A_ \alpha D^ \alpha u= f(x)\) \((x\in \mathbb{R}^ n)\) with bounded operators \(A_ \alpha\) from \(\mathbb{H}_{m-| \alpha|}\) into \(\mathbb{H}_ 0\), where \(\mathbb{H}_ m\subseteq\cdots\subseteq \mathbb{H}_ 1\subseteq \mathbb{H}_ 0\) are Hilbert spaces. The results of the article are some existence theorems in terms of the operator function \(R(\lambda)= \left[\sum_{|\alpha|\leq m}(i\lambda)^ \alpha A_ \alpha\right]^{-1}\).
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 567905
zbMATH Keywords: Hilbert spaces
zbMATH Keywords: existence theorems
zbMATH Keywords: operator function
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
cites work: Properties of solutions of ordinary differential equations in banach space
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description: scientific article; zbMATH DE number 567905