On Peano's theorem in Banach spaces |
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| Authors: | Petr Há jek |
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| Affiliation: | a Mathematical Institute, Czech Academy of Science, ?itná 25, 115 67 Praha 1, Czech Republic
b Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic |
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| Abstract: | We show that if X is an infinite-dimensional separable Banach space (or more generally a Banach space with an infinite-dimensional separable quotient) then there is a continuous mapping f:X→X such that the autonomous differential equation x′=f(x) has no solution at any point. |
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| Keywords: | 34A34 34G20 46B20 46B26 46G05 |
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