  We give sufficient conditions for a $ C^1_c $-local diffeomorphism between
Fr\'{e}chet spaces to be a global one. We extend the Clarke's theory of
generalized gradients to the more general setting of Fr\'{e}chet spaces. As a
consequence, we define the Chang Palais-Smale condition for Lipschitz functions
and show that a function which is bounded below and satisfies the Chang
Palais-Smale condition at all levels is coercive. We prove a version of the
mountain pass theorem for Lipschitz maps in the Fr\'{e}chet setting and show
that along with the Chang Palais-Smale condition we can obtain a global
diffeomorphism theorem.
