Surjectivity in Fréchet Spaces

Abstract

We prove surjectivity result in Frechet spaces of Nash–Moser type, that is, with uniform estimates over all seminorms. Our method works for functions, which are only continuous and strongly Gâteaux differentiable. We present the results in multi-valued setting exploring the relevant notions of map regularity. The key to our method is in geometrizing the tameness estimates and thus reducing the problem to a spectrum of problems on suitable Banach spaces. For solving the latter problems, we employ an abstract iteration scheme developed by the authors.