Surjectivity in Fréchet spaces

Abstract

We prove surjectivity result in Fréchet spaces of Nash-Moser type. That is, with uniform estimates over all semimorms. Our method works for functions which are only continuous and Gâteaux differentiable like in the recent result of Ekeland. We present the results in multi-valued setting exploring the relevant notions of map regularity.

The main correction in this version is clarifying that our definition of Gâteaux differentiability is stronger than the standard one

References in corpus (1)

• An implicit function theorem for non-smooth maps between Fréchet spaces

Cited by in corpus (2)

• A simple case within Nash-Moser-Ekeland theory
• Inverse Function Theorem in Fréchet Spaces