{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T05:54:56Z","timestamp":1726206896787},"reference-count":21,"publisher":"Oxford University Press (OUP)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1093\/imamci\/dny035","type":"journal-article","created":{"date-parts":[[2018,9,17]],"date-time":"2018-09-17T15:15:48Z","timestamp":1537197348000},"source":"Crossref","is-referenced-by-count":6,"title":["Stability of linear equations with differentiable operators in a hilbert space"],"prefix":"10.1093","author":[{"given":"Michael","family":"Gil\u2019","sequence":"first","affiliation":[{"name":"Department of Mathematics, Ben Gurion University of the Negev, P.0. Box, Beer-Sheva, Israel"}]}],"member":"286","published-online":{"date-parts":[[2018,9,18]]},"reference":[{"key":"key\n\t\t\t\t20180918063143_C1","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s00028-002-8083-0","article-title":"Indirect internal stabilization of weakly coupled evolution equations","volume":"66","author":"Alabau","year":"2002","journal-title":"J. Evol. Equ."},{"key":"key\n\t\t\t\t20180918063143_C2","volume-title":"The Theory of Lyapunov Exponents","author":"Bylov","year":"1966"},{"key":"key\n\t\t\t\t20180918063143_C3","article-title":"Evolution semigrous in dynamical systems and differential equations","volume-title":"Amer. Math. Soc., Math. Surv. Monographs","author":"Chicone","year":"1999"},{"key":"key\n\t\t\t\t20180918063143_C4","first-page":"451","article-title":"Stability of solutions of evolution equations","volume":"24","author":"Cialdea","year":"2013","journal-title":"Rend. Lincei Mat. Appl."},{"key":"key\n\t\t\t\t20180918063143_C5","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4224-6","volume-title":"Introduction to Infinite-Dimensional Systems Theory","author":"Curtain","year":"1995"},{"key":"key\n\t\t\t\t20180918063143_C6","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1093\/imamci\/dnq013","article-title":"Criteria for exponential stability of linear differential equations with positive evolution on ordered Banach spaces","volume":"27","author":"Dragan","year":"2010","journal-title":"IMA J. Math. Control Inform."},{"key":"key\n\t\t\t\t20180918063143_C7","doi-asserted-by":"crossref","first-page":"631","DOI":"10.3934\/eect.2013.2.631","article-title":"Regularity and stability of a wave equation with a strong damping & dynamic boundary conditions","volume":"2","author":"Fourrier","year":"2013","journal-title":"Evol. Equ. Control Theory"},{"key":"key\n\t\t\t\t20180918063143_C8","first-page":"949","article-title":"Stability of linear evolution equations in lattice normed spaces","volume":"15","author":"Gil\u2019","year":"1996","journal-title":"Zeitschrift fur Analysis"},{"key":"key\n\t\t\t\t20180918063143_C9","doi-asserted-by":"crossref","unstructured":"Gil\u2019, M.I. (2003) Operator Functions & Localization of Spectra. Lecture Notes In Mathematics, vol. 1830. Berlin: Springer.","DOI":"10.1007\/b93845"},{"key":"key\n\t\t\t\t20180918063143_C10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2013\/207581","article-title":"Integrally small perturbations of semigroups & stability of partial differential equations","volume":"2013","author":"Gil\u2019","year":"2013","journal-title":"Int. J. Partial Differential Equations"},{"key":"key\n\t\t\t\t20180918063143_C11","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.sysconle.2015.03.005","article-title":"Stability of linear nonautonomous multivariable systems with differentiable matrices","volume":"81","author":"Gil\u2019","year":"2015","journal-title":"Syst. Control Lett."},{"key":"key\n\t\t\t\t20180918063143_C12","first-page":"31","article-title":"On the operator equation $AX + XB = Q$","volume":"70","author":"Goldstein","year":"1978","journal-title":"Proc. Amer. Math. Soc."},{"key":"key\n\t\t\t\t20180918063143_C13","doi-asserted-by":"crossref","first-page":"1580","DOI":"10.1109\/TAC.2009.2015545","article-title":"Relaxed conditions for the exponential stability of a class of linear time-varying systems","volume":"54","author":"Jetto","year":"2009","journal-title":"IEEE Trans. Automat. Control"},{"key":"key\n\t\t\t\t20180918063143_C14","volume-title":"Linear Equations in a Banach Space","author":"Krein","year":"1971"},{"key":"key\n\t\t\t\t20180918063143_C15","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1007\/s10587-013-0060-y","article-title":"Stability for non-autonomous linear evolution equations with Lp-maximal regularity","volume":"63","author":"Laasri","year":"2013","journal-title":"Czechoslovak Math. J."},{"key":"key\n\t\t\t\t20180918063143_C16","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1016\/j.automatica.2006.10.014","article-title":"A numerical sufficiency test for the asymptotic stability of linear time-varying systems","volume":"43","author":"Mullhaupt","year":"2007","journal-title":"Automatica"},{"key":"key\n\t\t\t\t20180918063143_C17","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/s13348-017-0192-8","article-title":"Convergence & stability analyses of hierarchic models of dissipative second order evolution equations","volume":"68","author":"Nicaise","year":"2017","journal-title":"Collect. Math."},{"key":"key\n\t\t\t\t20180918063143_C18","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719864","volume-title":"Strongly Stabilizable Distributed Parameter Systems","author":"Oostveen","year":"2000"},{"key":"key\n\t\t\t\t20180918063143_C19","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5561-1","volume-title":"Semigroups of Linear Operators and Applications to Partial Differential Equations","author":"Pazy","year":"1983"},{"key":"key\n\t\t\t\t20180918063143_C20","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1002\/(SICI)1097-0312(199602)49:2<177::AID-CPA3>3.0.CO;2-B","article-title":"Asymptotic stability for nonautonomous wave equation","volume":"XLXX","author":"Pucci","year":"1996","journal-title":"Comm. Pure Appl. Math."},{"key":"key\n\t\t\t\t20180918063143_C21","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/BF01211523","article-title":"On the stability of slowly time-varying linear systems","volume":"7","author":"Solo","year":"1994","journal-title":"Mathemat. Control Signals Syst."}],"container-title":["IMA Journal of Mathematical Control and Information"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/imamci\/advance-article-pdf\/doi\/10.1093\/imamci\/dny035\/25790687\/dny035.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,24]],"date-time":"2019-10-24T05:29:30Z","timestamp":1571894970000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imamci\/advance-article\/doi\/10.1093\/imamci\/dny035\/5097007"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,18]]},"references-count":21,"URL":"https:\/\/doi.org\/10.1093\/imamci\/dny035","relation":{},"ISSN":["0265-0754","1471-6887"],"issn-type":[{"value":"0265-0754","type":"print"},{"value":"1471-6887","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9,18]]}}}