LAUSR

We establish sufficient conditions for a C c 1 $$ {C}_c^1 $$ -local diffeomorphism between Fréchet spaces to be a global diffeomorphism. We extend Clarke’s theory of generalized gradients to more general Fréchet 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 the Lipschitz functions in Fréchet spaces and show that, under the Chang–Palais–Smale condition, it is possible to obtain a theorem on global diffeomorphism.