Counterexample to Peano's theorem in infinite-dimensional \(F'\)-spaces

DOI10.1007/BF02356072zbMath0914.47047OpenAlexW1980104634WikidataQ124982724 ScholiaQ124982724MaRDI QIDQ1277429

Stanislav Shkarin

Publication date: 1 March 1999

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02356072

zbMATH Keywords

Cauchy problemordinary differential equation\(F'\)-spacenonnormable Fréchet space

Mathematics Subject Classification ID

General theory of ordinary differential operators (47E05) Locally convex Fréchet spaces and (DF)-spaces (46A04)

Related Items (3)

ON THE SOLVABILITY OF HAMILTON'S EQUATIONS IN HILBERT SPACES ⋮ Lineability and spaceability for the weak form of Peano’s theorem and vector-valued sequence spaces ⋮ Extension operator for subspaces of vector spaces over the field \(\mathbb{F}_2\)

Cites Work

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• Peano's theorem in Banach spaces
• Ordinary differential equations with a continuous right-hand side in Fréchet spaces
• Peano's theorem fails for infinite-dimensional Fréchet spaces
• SOME RESULTS ON SOLVABILITY OF ORDINARY LINEAR DIFFERENTIAL EQUATIONS IN LOCALLY CONVEX SPACES
• On the nonexistence of solutions of differential equations in nonreflexive spaces
• On Peano's theorem in locally convex spaces
• Chebyshev-Haar systems in the theory of discontinuous Kellogg kernels
• Continuous Extensions
• A Selection Theorem

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