Self-adjoint boundary-value problems on time-scales
In this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form $$ L u := -[p u^{ abla}]^{Delta} + qu, $$ on an arbitrary, bounded time-scale $mathbb{T}$, for suitable functions $p,q$, together with suitable boundary conditions. We show that, with a suitable...
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Texas State University
2007-12-01
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doaj-76e8b8158c08442394f5b4d2a34ab2f42020-11-24T22:38:34ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912007-12-012007175110Self-adjoint boundary-value problems on time-scalesBryan P. RynneFordyce A. DavidsonIn this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form $$ L u := -[p u^{ abla}]^{Delta} + qu, $$ on an arbitrary, bounded time-scale $mathbb{T}$, for suitable functions $p,q$, together with suitable boundary conditions. We show that, with a suitable choice of domain, this operator can be formulated in the Hilbert space $L^2(mathbb{T}_kappa)$, in such a way that the resulting operator is self-adjoint, with compact resolvent (here, "self-adjoint" means in the standard functional analytic meaning of this term). Previous discussions of operators of this, and similar, form have described them as self-adjoint, but have not demonstrated self-adjointness in the standard functional analytic sense.http://ejde.math.txstate.edu/Volumes/2007/175/abstr.htmlTime-scalesboundary-value problemself-adjoint linear operatorsSobolev spaces |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Bryan P. Rynne Fordyce A. Davidson |
spellingShingle |
Bryan P. Rynne Fordyce A. Davidson Self-adjoint boundary-value problems on time-scales Electronic Journal of Differential Equations Time-scales boundary-value problem self-adjoint linear operators Sobolev spaces |
author_facet |
Bryan P. Rynne Fordyce A. Davidson |
author_sort |
Bryan P. Rynne |
title |
Self-adjoint boundary-value problems on time-scales |
title_short |
Self-adjoint boundary-value problems on time-scales |
title_full |
Self-adjoint boundary-value problems on time-scales |
title_fullStr |
Self-adjoint boundary-value problems on time-scales |
title_full_unstemmed |
Self-adjoint boundary-value problems on time-scales |
title_sort |
self-adjoint boundary-value problems on time-scales |
publisher |
Texas State University |
series |
Electronic Journal of Differential Equations |
issn |
1072-6691 |
publishDate |
2007-12-01 |
description |
In this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form $$ L u := -[p u^{ abla}]^{Delta} + qu, $$ on an arbitrary, bounded time-scale $mathbb{T}$, for suitable functions $p,q$, together with suitable boundary conditions. We show that, with a suitable choice of domain, this operator can be formulated in the Hilbert space $L^2(mathbb{T}_kappa)$, in such a way that the resulting operator is self-adjoint, with compact resolvent (here, "self-adjoint" means in the standard functional analytic meaning of this term). Previous discussions of operators of this, and similar, form have described them as self-adjoint, but have not demonstrated self-adjointness in the standard functional analytic sense. |
topic |
Time-scales boundary-value problem self-adjoint linear operators Sobolev spaces |
url |
http://ejde.math.txstate.edu/Volumes/2007/175/abstr.html |
work_keys_str_mv |
AT bryanprynne selfadjointboundaryvalueproblemsontimescales AT fordyceadavidson selfadjointboundaryvalueproblemsontimescales |
_version_ |
1725713048958664704 |