The Morse-Sard-Brown Theorem for Functionals on Bounded Fréchet-Finsler Manifolds

summary:In this paper we study Lipschitz-Fredholm vector fields on bounded Fréchet-Finsler manifolds. In this context we generalize the Morse-Sard-Brown theorem, asserting that if $M$ is a connected smooth bounded Fréchet-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 $\mathbb {R}$