Global inversion theorems via coercive functionals on metric spaces

Global inversion and covering maps on length spaces

“…On the other hand Katriel [8], using an abstract Mountain-Pass theorem, obtained global inversion results for local homeomorphisms defined on certain metric spaces. In our previous work [9], we have considered the problem of global inversion for the case of mappings between metric spaces with nice local structure, the so-called locally strongly R-contractible spaces (see also [10] for related results). The relevant problem in this case is to find conditions of metric nature under which a local homeomorphism is a covering map.…”

On a global diffeomorphism between two Banach spaces and some application

“…Thus the main problem which must be tackled is to make a local diffeomorphism a global one. The approach towards answering this question may be undertaken within critical point theory by using mountain pass technique as suggested by [11] and continued in [7] or by auxiliary coercive functionals as started by [17] and next developed for a case of more general spaces in [5]. The result of [11] most closely related to ours is as follows (provided as in [9], Theorem 5.4)…”