GLOBAL BIFURCATION OF AN ELASTIC CONDUCTING ROD IN A MAGNETIC-FIELD

We study the equilibrium states of a nonlinearly elastic conducting ro d in a magnetic field, a problem we have considered in several previou s papers. We are now able to prove a global bifurcation theorem for th is problem. To do this, two difficulties must be overcome. The first i s the presence of the rotation group SO(2) as a symmetry group for the problem. The second is that, for some values of certain parameters, t he linearized problem is a nonstandard eigenvalue problem. The former difficulty is overcome by applying an idea due to Healey, who observed the existence of an additional symmetry in a related problem first po sed by the present author. The latter problem is handled by using some nonstandard tools from functional analysis.