Equilibria for set-valued maps on nonsmooth domains
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- Ben-El-Mechaiekh, H. J. fixed point theory appl. (2008) 4: 177. doi:10.1007/s11784-008-0074-5
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A set-valued map defined on a compact lipschitzian retract of a normed space with nontrivial Euler characteristic and satisfying (i) a strong graph approximation property and (ii) a tangency condition expressed in terms of Clarke’s tangent cone, admits an equilibrium. This result extends in a simple way known solvability theorems to a large class of nonconvex set-valued maps defined on nonsmooth domains.