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On Lipschitz conditions for ordinary differential equations in Fréchet spaces. (English) Zbl 0930.34042
From the author’s abstract: “An existence and uniqueness theorem for ordinary differential equations in Fréchet spaces using Lipschitz conditions is formulated with a generalized distance and row-finite matrices”.
Reviewer: A.Kufner (Praha)

MSC:
34G20 Nonlinear differential equations in abstract spaces
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References:
[1] K. Deimling: Ordinary differential equations in Banach spaces. Lecture Notes in Mathematics 596, Springer, 1977. · Zbl 0361.34050
[2] Sh. T. Dzhabbharov: A generalized contraction-mapping principle and infinite systems of differential equations. Diff. Eqs. 26 (1990), 944-952.
[3] A. N. Godunov, A. P. Durkin: Differential equations in linear topological spaces. Moscow Univ. Math. Bull. 24 (1969), 93-100. · Zbl 0245.34053
[4] G. Herzog: Über gewöhnliche Differentialgleichungen in Frécheträumen. Dissertation, Univ. Karlsruhe, 1992. · Zbl 0832.34055
[5] G. Herzog: On ordinary linear differential equations in \(J\). Demonstratio Math. 28 (1995), 383-398. · Zbl 0838.34075
[6] 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
[7] K. H. Körber: Das Spektrum zeilenfiniter Matrizen. Math. Ann. 181 (1969), 8-34. · Zbl 0211.44301
[8] R. Lemmert, Ä. Weckbach: Charakterisierungen zeilenendlicher Matrizen mit abzählbarem Spektrum. Math. Z. 188 (1984), 119-124. · Zbl 0554.47015
[9] R. Lemmert: On ordinary differential equations in locally convex spaces. Nonlinear Analysis 10 (1986), 1385-1390. · Zbl 0612.34056
[10] S. G. Lobanov: Solvability of linear ordinary differential equations in locally convex spaces. Moscow Univ. Math. Bull. 35 (1980), 1-5. · Zbl 0461.34046
[11] K. Moszyński, A. Pokrzywa: Sur les systèmes infinis d’équations différentielles ordinaires dans certains espaces de Fréchet. Dissertationes Math. CXV, 1974.
[12] J. Schröder: Iterationsverfahren bei allgemeinerem Abstandsbegriff. Math. Z. 66 (1956), 111-116. · Zbl 0073.33503
[13] H. Ulm: Elementarteilertheorie unendlicher Matrizen. Math. Ann. 114 (1937), 493-505. · Zbl 0017.09901
[14] J. H. Williamson: Spectral representation of linear transformations in \(\omega \). Proc. Cambridge Philos. Soc. 47 (1951), 461-472. · Zbl 0042.12201
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