D-orientation sequences for continuous functions and nonlinear complementarity problems

We introduce the new concept of d-orientation sequence for continuous functions. It is shown that if there does not exist a d-orientation sequence for a continuous function, then the corresponding complementarity problem (CP) has a solution. We believe that such a result characterizes an intrinsic property of CPs. As the concept of ``exceptional family of elements'', the notion of ``d-orientation sequence of a function'' is also a powerful tool for investigating the existence theorems of CPs. We use this new tool to establish, among other things, a new existence result for a class of P -mapping CPs. Ó 1999 Published by Elsevier Science Inc. All rights reserved.