Equilibria on $L$-retracts in Riemannian manifolds

Abstract

We introduce a class of subsets of Riemannian manifolds called the $L$-retract. Next we consider a topological degree for set-valued upper semicontinuous maps defined on open sets of compact $L$-retracts in Riemannian manifolds. Then, we present a theorem on the existence of equilibria (or zeros) of an upper semicontinuous set-valued map with nonempty closed convex values satisfying the tangency condition defined on a compact $L$-retract in a Riemannian manifold