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.