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- W2056367070 abstract "Previous article Next article The Perron Condition for Differential-Sifference Equations in a Hilbert SpaceRichard DatkoRichard Datkohttps://doi.org/10.1137/0512070PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe Perron condition, or bounded input-bounded output criterion for linear systems, is extended to a class of linear differential-difference equations in a Hilbert space.[1] Richard Bellman, On an application of a Banach-Steinhaus theorem to the study of the boundedness of solutions of non-linear differential and difference equations, Ann. of Math. (2), 49 (1948), 515–522 10,121b 0031.39902 CrossrefISIGoogle Scholar[2] R. W. Brockett, Finite Dimensional Linear Systems, John Wiley, New York, 1970 0216.27401 Google Scholar[3] J. L. Daletskii and , M. G. Krein, Stability of Solutions of Differential Equations in a Banach Space, Izdat. Nauka, Moscow, 1970, (In Russian.) Google Scholar[4] Richard Datko, Uniform asymptotic stability of evolutionary processes in a Banach space, SIAM J. Math. Anal., 3 (1972), 428–445 10.1137/0503042 47:9004 0241.34071 LinkGoogle Scholar[5] Richard Datko, Representation of solutions and stability of linear differential-difference equations in a Banach space, J. Differential Equations, 29 (1978), 105–166 58:6619 0379.34049 CrossrefISIGoogle Scholar[6] A. Halanay, Differential equations: Stability, oscillations, time lags, Academic Press, New York, 1966xii+528 35:6938 0144.08701 Google Scholar[7] Jack Hale, Theory of functional differential equations, Springer-Verlag, New York, 1977x+365 58:22904 0352.34001 CrossrefGoogle Scholar[8] Einar Hille and , Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957xii+808 19,664d Google Scholar[9] O. Perron, Die Stabilitätsfrage bei Differentialgleichungen, Math. Z., 32 (1930), 703–728 56.1040.01 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Volume 12, Issue 6| 1981SIAM Journal on Mathematical Analysis799-961 History Submitted:20 December 1978Accepted:11 February 1981Published online:17 February 2012 InformationCopyright © 1981 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0512070Article page range:pp. 842-852ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics" @default.
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- W2056367070 title "The Perron Condition for Differential-Sifference Equations in a Hilbert Space" @default.
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