Surjectivity in Fr\'echet spaces

TL;DR

This paper establishes surjectivity results in Nash-Moser type Fréchet spaces, extending to continuous Gâteaux differentiable functions and multi-valued maps, with uniform estimates across all semimorms.

Contribution

It introduces a surjectivity theorem for functions in Fréchet spaces of Nash-Moser type, applicable to continuous Gâteaux differentiable and multi-valued maps, with uniform estimates.

Findings

Proves surjectivity in Nash-Moser type Fréchet spaces.

Extends results to continuous Gâteaux differentiable functions.

Includes multi-valued map regularity analysis.

Abstract

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