Gamma-Convergence and Saddle Points

We prove a theorem asserting, roughly speaking, that if a sequence of functionals converges to a limiting functional (in the sense of Gamma-convergence, a natural and widely-used notion in the calculus of variations), and if the limiting functional has a nondegenerate critical point, then the approximating functionals have an associated critical point. This is an analog for saddle points of a theorem about local minimizers, due to Kohn and Sternberg, that has been known for about 20 years. We apply the theorem to prove the existence of certain solutions of Ginzburg-Landau equations. This is joint work with Peter Sternberg