  This paper concerns upper estimates of the projectional coderivative of
implicit mappings and corresponding applications on analyzing the relative
Lipschitz-like property. Under different constraint qualifications, we provide
upper estimates of the projectional coderivative for solution mappings of
parametric systems. For the solution mapping of affine variational
inequalities, a generalized critical face condition is obtained for sufficiency
of its Lipschitz-like property relative to a polyhedral set within its domain
under a constraint qualification. The equivalence between the relative
Lipschitz-like property and the local inner-semicontinuity for polyhedral
multifunctions is also demonstrated. For the solution mapping of linear
complementarity problems with a $Q_0$-matrix, we establish a sufficient and
necessary condition for the Lipschitz-like property relative to its convex
domain via the generalized critical face condition and its combinatorial
nature.
