  Existence and regularity of minimizers in elliptic free boundary problems
have been extensively studied in the literature. We initiate the corresponding
study of higher critical points by considering a superlinear free boundary
problem related to plasma confinement. The associated energy functional is
nondifferentiable, and therefore standard variational methods cannot be used
directly to prove the existence of critical points. Here we obtain a nontrivial
generalized solution $u$ of mountain pass type as the limit of mountain pass
points of a suitable sequence of $C^1$-functionals approximating the energy. We
show that $u$ minimizes the energy on the associated Nehari manifold and use
this fact to prove that it is nondegenerate. We use the nondegeneracy of $u$ to
show that it satisfies the free boundary condition in the viscosity sense.
Moreover, near any free boundary point that has a measure-theoretic normal, the
free boundary is a smooth surface, and hence the free boundary condition holds
in the classical sense.
