Mountain pass theorems and global homeomorphism theorems. (English) Zbl 0834.58007

Katriel, Guy

Ann. Inst. Henri Poincaré, Anal. Non Linéaire 11, No. 2, 189-209 (1994).

Summary: We show that mountain-pass theorems can be used to derive global homeomorphism theorems. Two new mountain-pass theorems are proved, generalizing the “smooth” mountain-pass theorems, one applying in locally compact topological spaces, using Hofer’s concept of mountain- pass point, and another applying in complete metric spaces, using a generalized notion of critical point similar to the one introduced by Ioffe and Schwartzman. These are used to prove global homeomorphism theorems for certain topological and metric spaces, generalizing known global homeomorphism theorems for mappings between Banach spaces.

MSC:

58C15	Implicit function theorems; global Newton methods on manifolds
58E05	Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces

Keywords:

mountain-pass theorems; global homeomorphism theorems

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