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Counterexample to Peano's theorem in infinite-dimensionalF′-spaces |
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| Authors: | S A Shkarin |
| Institution: | (1) M. V. Lomonosov Moscow State University, Moscow, USSR |
| Abstract: | LetE be a nonnormable Fréchet space, and letE′ be the space of all continuous linear functionals onE in the strong topology. A continuous mappingf:E′→E′ such that for anyt 0∈ℝ,x 0∈E′, the Cauchy problemx=f(x), x(t 0 )=x 0 has no solutions is constructed. Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 128–137, July, 1997. Translated by V. N. Dubrovsky |
| Keywords: | Cauchy problem ordinary differential equation locally convex space Fréchet space F′ -space |
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