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Title: On Lipschitz conditions for ordinary differential equations in Fréchet spaces (English)
Author: Herzog, Gerd
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 48
Issue: 1
Year: 1998
Pages: 95-103
Summary lang: English
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Category: math
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Summary: We will give an existence and uniqueness theorem for ordinary differential equations in Fréchet spaces using Lipschitz conditions formulated with a generalized distance and row-finite matrices. (English)
MSC: 34G20
MSC: 46G05
idZBL: Zbl 0930.34042
idMR: MR1614009
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Date available: 2009-09-24T10:11:30Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/127402
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Reference: [De] K. Deimling: Ordinary differential equations in Banach spaces.Lecture Notes in Mathematics 596, Springer, 1977. Zbl 0361.34050, MR 0463601, 10.1007/BFb0091643
Reference: [Dz] Sh. T. Dzhabbharov: A generalized contraction-mapping principle and infinite systems of differential equations.Diff. Eqs. 26 (1990), 944–952. MR 1074257
Reference: [Go] A. N. Godunov, A. P. Durkin: Differential equations in linear topological spaces.Moscow Univ. Math. Bull. 24 (1969), 93–100. MR 0254397
Reference: [He1] G. Herzog: Über gewöhnliche Differentialgleichungen in Frécheträumen.Dissertation, Univ. Karlsruhe, 1992. Zbl 0832.34055
Reference: [He2] G. Herzog: On ordinary linear differential equations in $J$.Demonstratio Math. 28 (1995), 383–398. MR 1346844
Reference: [He3] G. Herzog: On existence and uniqueness conditions for ordinary differential equations in Fréchet spaces.Studia Sci. Math. Hungar. 32 (1996), 367–375. Zbl 0880.34066, MR 1432178
Reference: [Ko] K. H. Körber: Das Spektrum zeilenfiniter Matrizen.Math. Ann. 181 (1969), 8–34. MR 0262863, 10.1007/BF01351175
Reference: [Le1] R. Lemmert, Ä. Weckbach: Charakterisierungen zeilenendlicher Matrizen mit abzählbarem Spektrum.Math. Z. 188 (1984), 119–124. MR 0767369, 10.1007/BF01163880
Reference: [Le2] R. Lemmert: On ordinary differential equations in locally convex spaces.Nonlinear Analysis 10 (1986), 1385–1390. Zbl 0612.34056, MR 0869547, 10.1016/0362-546X(86)90109-4
Reference: [Lo] S. G. Lobanov: Solvability of linear ordinary differential equations in locally convex spaces.Moscow Univ. Math. Bull. 35 (1980), 1–5. Zbl 0461.34046, MR 0570579
Reference: [Mo] K. Moszyński, A. Pokrzywa: Sur les systèmes infinis d’équations différentielles ordinaires dans certains espaces de Fréchet.Dissertationes Math. CXV, 1974.
Reference: [Sch] J. Schröder: Iterationsverfahren bei allgemeinerem Abstandsbegriff.Math. Z. 66 (1956), 111–116. MR 0083816, 10.1007/BF01186599
Reference: [Ul] H. Ulm: Elementarteilertheorie unendlicher Matrizen.Math. Ann. 114 (1937), 493–505. Zbl 0017.09901, MR 1513152, 10.1007/BF01594190
Reference: [Wi] J. H. Williamson: Spectral representation of linear transformations in $\omega $.Proc. Cambridge Philos. Soc. 47 (1951), 461–472. Zbl 0042.12201, MR 0042615
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