  A bifurcation about the uniqueness of a solution of a singularly perturbed
free boundary problem of phase transition associated with the p-Laplacian,
subject to given boundary condition is proved in this paper. We show this
phenomenon by proving the existence of a third solution through the Mountain
Pass Lemma when the boundary data decreases below a threshold. In the second
part, we prove the convergence of an evolution to stable solutions, and show
the Mountain Pass solution is unstable in this sense.
