Higher energy solutions in the theory of phase transitions: A variational approach

We establish the existence of a higher-energy solution to the vector Ginzbu rg Landau equation with a triple-well potential on a hounded and smooth dom ain on the plane. This solution is obtained by a linking argument. In imple menting this variational approach we make several considerations on the dyn amics of the negative gradient flow. In particular, we use the Conlty index to contruct a suitable one-dimensional invariant set. This solution has Mo rse index two in the nondegenerate case. We discuss its structure in connec tion with the so-called triple-junction configurations. (C) 2001 Academic P ress.