Exceptional Families and Nonlinear Complementarity Problems.

Abstract: In this paper, we study the following Linear 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(τ, α, β) -mapping or a semi-monotone mapping, a sufficiently condition is established to assure the existence and boundedness of solution curve [Copyright &y& Elsevier]