The authors consider the space L(D) consisting of Lipschitz continuous mappings from D to the Euclidean n-space ℝn, D being an open bounded subset of ℝn. Let F belong to L(D) and suppose that nx solves the equation F(x)=0. In case that the generalized Jacobian of F at nx is nonsingular (in the sense of Clarke), the authors show that for G near F (with respect to a natural norm) the system G(x)=0 has a unique solution, say x(G), in a neighborhood of nx. Moreover, the mapping which sends G to x(G) is shown to be Lipschitz continuous. The latter result is connected with the sensitivity of strongly stable stationary points in the sense of Kojima; here, the linear independence constraint qualification is assumed to be satisfied.
