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Critical points for vector-valued functions

Lucchetti R., Revalski J., Thera M.

Control and Cybernetics

2002

Vol. 31, no 3

545-555

This paper contains a mountain pass theorem for continuous mappings, defined on a complete metric space and taking values in a real Banach space, ordered by a closed convex cone. We use the concept of critical point introduced by Degiovanni, Lucchetti and Ribarska, and we furnish a variant of their result, allowing for a localization both of the critical point and of the critical value.