Coercivity Conditions in Nonlinear Complementarity Problems

If F:Rⁿ → Rⁿ is a continuous mapping on a closed, convex cone K of Rⁿ, it is shown that very weak restrictions on the growth of F (coercivity conditions) guarantee the existence of a solution to the nonlinear complementarily problem : for each z in Rⁿ, find an x^ * in K such that Fx^ * - z belongs to the polar of K and x^ * is orthogonal to Fx^ * - z. If K is Rⁿ, then this problem reduces to finding conditions on F which guarantee that F maps Rⁿ onto Rⁿ.