A partial converse to Hadamard's theorem on homeomorphisms.
A theorem by Hadamard gives a two-part condition under which a map from one Banach space to another is a homeomorphism. The theorem, while often very useful, is incomplete in the sense that it does not explicitly specify the family of maps for which the condition is met. Here, under a typically weak additional assumption on the map, the author shows that Hadamard's condition is met if and only if the map is a homeomorphism with a Lipschitz continuous inverse. An application is given concerning the relation between the stability of a nonlinear system and the stability of related linear systems.
scientific article; zbMATH DE number 1885801