Ekeland's inverse function theorem in graded Fréchet spaces revisited for multifunctions

Abstract

In this paper, we present some implicit function theorems for set-valued mappings between Fréchet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions of differential equations in Fréchet spaces with non-smooth data is given.

Revised version