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 Mat. Sb., 1990, Volume 181, Number 9, Pages 1183–1195 (Mi msb1216)

This article is cited in 10 scientific papers (total in 10 papers)

Some results on solvability of ordinary linear differential equations in locally convex spaces

S. A. Shkarin

M. V. Lomonosov Moscow State University

Abstract: Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x=Ax$, $x(0)=x_0$, with respect to functions $x\colon\mathbf R\to E$. It is proved that if $E\in\Gamma$, then $E\times\mathbf R^A\in\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Fréchet spaces, each not isomorphic to $\mathbf R^\infty$, does not belong to $\Gamma$.

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English version:
Mathematics of the USSR-Sbornik, 1992, 71:1, 29–40

Bibliographic databases:

UDC: 517.9
MSC: Primary 34A10, 34G10; Secondary 46A05
Received: 22.06.1989

Citation: S. A. Shkarin, “Some results on solvability of ordinary linear differential equations in locally convex spaces”, Mat. Sb., 181:9 (1990), 1183–1195; Math. USSR-Sb., 71:1 (1992), 29–40

Citation in format AMSBIB
\Bibitem{Shk90} \by S.~A.~Shkarin \paper Some results on solvability of ordinary linear differential equations in locally convex spaces \jour Mat. Sb. \yr 1990 \vol 181 \issue 9 \pages 1183--1195 \mathnet{http://mi.mathnet.ru/msb1216} \zmath{https://zbmath.org/?q=an:0745.34063|0723.34043} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992SbMat..71...29S} \transl \jour Math. USSR-Sb. \yr 1992 \vol 71 \issue 1 \pages 29--40 \crossref{https://doi.org/10.1070/SM1992v071n01ABEH002126} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992HJ82500003} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. G. Lobanov, “Picard's theorem for ordinary differential equations in locally convex spaces”, Russian Acad. Sci. Izv. Math., 41:3 (1993), 465–487
2. S. G. Lobanov, O. G. Smolyanov, “Ordinary differential equations in locally convex spaces”, Russian Math. Surveys, 49:3 (1994), 97–175
3. Bogachev V., “Deterministic and Stochastic Differential-Equations in Infinite-Dimensional Spaces”, Acta Appl. Math., 40:1 (1995), 25–93
4. T. S. Rybunikova, “On Linear Row-Finite Systems of Stochastic Differential Equations”, Theory Probab Appl, 45:3 (2001), 539
5. T. S. Rybnikova, “On Infinite Systems of Linear Autonomous and Nonautonomous Stochastic Equations”, Math. Notes, 71:6 (2002), 815–824
6. Shkarin S.A., “Compact Perturbations of Linear Differential Equations in Locally Convex Spaces”, Studia Math., 172:3 (2006), 203–227
7. PawełDomański, Michael Langenbruch, “On the abstract Cauchy problem for operators in locally convex spaces”, RACSAM, 2011
8. S. N. Mishin, “Homogeneous differential-operator equations in locally convex spaces”, Russian Math. (Iz. VUZ), 61:1 (2017), 22–38
9. Bogachev V. Smolyanov O., “Topological Vector Spaces and Their Applications”, Topological Vector Spaces and Their Applications, Springer Monographs in Mathematics, Springer, 2017, 1–456
10. S. N. Mishin, “Generalization of the Lagrange Method to the Case of Second-Order Linear Differential Equations with Constant Operator Coefficients in Locally Convex Spaces”, Math. Notes, 103:1 (2018), 75–88
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