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On Nash–Moser–Ekeland Inverse Mapping Theorem

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Abstract

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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Funding

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

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Authors and Affiliations

  1. NTIS and Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 22, 306 14, Pilsen, Czech Republic

    Radek Cibulka

  2. Mathematical Institute of Czech Academy of Sciences, žitná 25, 115 67, Praha 1, Czech Republic

    Marián Fabian

Authors
  1. Radek Cibulka
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  2. Marián Fabian
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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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  • DOI: https://doi.org/10.1007/s10013-019-00342-w

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