  We prove that a certain class of elliptic free boundary problems, which
includes the Prandtl-Batchelor problem from fluid dynamics as a special case,
has two distinct nontrivial solutions for large values of a parameter. The
first solution is a global minimizer of the energy. The energy functional is
nondifferentiable, so standard variational arguments cannot be used directly to
obtain a second nontrivial solution. We obtain our second solution as the limit
of mountain pass points of a sequence of $C^1$-functionals approximating the
energy. We use careful estimates of the corresponding energy levels to show
that this limit is neither trivial nor a minimizer.
