The Properties of a Homotopy Path of Nonlinear Complementarity Problems

In this paper, we study the following nonlinear complementarity problem: f : R-n -> R-n, find x >= 0, such that f(x) >= 0, x(T) f(x)=0. We use Poineare-Bohn's homotopy invariance theorem of degree to derive an alternative theorem, and give a new exceptional families. Based on this result, for the nonlinear complementarity problems with a quasi-(P)*-mapping or a (P(tau, alpha, beta)) -mapping, a sufficiently condition is established to assure the existence and boundedness of solution curve.