Herzog, Gerd On Lipschitz conditions for ordinary differential equations in Fréchet spaces. (English) Zbl 0930.34042 Czech. Math. J. 48, No. 1, 95-103 (1998). 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) Cited in 5 Documents MSC: 34G20 Nonlinear differential equations in abstract spaces Keywords:ordinary differential equation; Fréchet space; existence theorem; uniqueness theorem PDF BibTeX XML Cite \textit{G. Herzog}, Czech. Math. J. 48, No. 1, 95--103 (1998; Zbl 0930.34042) Full Text: DOI EuDML OpenURL 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.