Mathematical Notes

, Volume 62, Issue 1, pp 108–115 | Cite as

Counterexample to Peano's theorem in infinite-dimensionalF′-spaces

  • S. A. Shkarin


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 anyt0∈ℝ,x0E′, the Cauchy problemx=f(x), x(t0)=x0 has no solutions is constructed.

Key words

Cauchy problem ordinary differential equation locally convex space Fréchet space F′-space 


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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • S. A. Shkarin
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityMoscowUSSR

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