On the representation of the solutions of some strongly degenerating differential equation of second order in Hilbert space
type: Item
instance of: scholarly article
title: On the representation of the solutions of some strongly degenerating differential equation of second order in Hilbert space
zbMATH Open document ID: 0647.34073
DOI: 10.1007/BF00972020
published in: Lithuanian Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: In a separable Hilbert space H the equation (1) \(z\quad n(u''+Au)-c\quad 2u=0\) is studied. A is unbounded, self-adjoint and negative-definite operator in H with an everywhere dense domain D(A) in H. The compact inverse \(A^{-1}\) exists. A function u(z) for \(z>0\) and u(z)\(\in D(A)\) is a solution to (1) when this equation is satisfied in (0,\(\infty)\). A system of solutions to (1) is constructed and the asymptotic behaviour in the neighbourhood of \(z=0\) is studied. The results are obtained in a form of Laplace integrals and asymptotic series.
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 4056126
zbMATH Keywords: separable Hilbert space
zbMATH Keywords: Laplace integrals
Wikidata QID: Q115394656
author: Bronius Kvedaras
reviewed by: Tadeusz Dłotko
MaRDI profile type: Publication
cites work: Q3310260
cites work: Q3712691
cites work: Q5336417
full work available at URL: https://doi.org/10.1007/bf00972020
OpenAlex ID: W2049558846
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description: scientific article; zbMATH DE number 4056126