On Nash–Moser–Ekeland Inverse Mapping Theorem


We present a criterion for local surjectivity of mappings between graded Fréchet spaces in the spirit of a well-known criterion in Banach spaces. As applications, we get “hard inverse mapping theorem” in the flavor of Nash–Moser. The technology of proofs was strongly influenced by a recent paper of Ekeland.

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The second author was supported by the grant of GAČR 17-00941S and by RVO: 67985840.

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Correspondence to Radek Cibulka.

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Dedicated to the 80th birthday of Alex D. Ioffe

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Cibulka, R., Fabian, M. On Nash–Moser–Ekeland Inverse Mapping Theorem. Vietnam J. Math. 47, 527–545 (2019). https://doi.org/10.1007/s10013-019-00342-w

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  • Fréchet space
  • Nash–Moser inverse mapping theorem
  • Local surjection
  • Metric regularity

Mathematics Subject Classification (2010)

  • 58C15
  • 47J07
  • 46T20