Abstract. We study several properties of a homotopy solution mapping, based on Zhang and Zhang's homotopy formulation, for continuous nonlinear complementarity problems with such nonmonotone maps as quasi-monotone, E 0-, and exceptional regular functions. For these classes of complementarity problems, we establish several sufficient conditions to assure the nonemptyness and boundedness of the homotopy solution mapping. Under the P 0 property, all these sufficient conditions also guarantee the uniqueness and continuity of the homotopy solution mapping, and hence the range of this mapping forms a continuous path passing through an arbitrary point in R
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