The Morse Sard Brown Theorem for Functionals on Bounded Fr\{e}chet Finsler Manifolds
In this paper we study Lipschitz Fredholm vector fields on Bounded Fr\{e}chet Finsler manifolds. In this context we generalize the Morse Sard Brown theorem, asserting that if $M$ is a connected smooth bounded Fr\{e}chet Finsler manifold endowed with a connection \mathcal{K} and if \xi$ is a smooth Lipschitz Fredholm vector field on $M$ with respect to \mathcal{K} which satisfies condition (WCV) Then, for any smooth functional $l$ on $M$ which is associated to \xi$ the set of the critical values of $l$ is of first category in \mathbb{R} Therefore, the set of the regular values of $l$ is a residual Baire subset of \mathbb{R}