Direction and stability of bifurcation branches for variational inequalities

We consider a class of variational inequalities with a multidimensional bifurcation parameter under assumptions guaranteeing the existence of smooth families of nontrivial solutions bifurcating from the set of trivial solutions. The direction of bifurcation is shown in a neighborhood of bifurcation points of a certain type. In the case of potential operators, also the stability and instability of bifurcating solutions and of the trivial solution is described in the sense of minima of the potential. In particular, an exchange of stability is observed.