Kamenskii M. & Quincampoix M.


Titre: "Existence of Equilibria on Epilipschitz sets without invariance conditions."


Abstract: We provide a new result of existence of equilibria of a single-valued Lipschitz function f on a compact set K of Rⁿ which is locally the epigraph of a Lipschitz functions (such a set is called epilichitz set). The main point of our result lies in the fact that we do not impose that f(x) is an "inward vector" for all point x of the boundary of K. Some extensions of the existence of equilibria result are also discussed for continuous functions and set-valued maps.