Structural and stability properties of P-0 nonlinear complementarity problems

We consider P-0 nonlinear complementarity problems and study the connectedn ess and stability of the solutions by applying degree theory and the Mounta in Pass Theorem to a smooth reformulation of the complementarity problem. W e show that the solution set is connected and bounded if a bounded isolated component of the solution set exists and that a solution is locally unique if and only if it is globally unique. Furthermore, we prove that a solutio n is stable in Ha's sense if and only if it is globally unique, while the c omplementarity problem is stable if and only if the solution set is bounded .