  In this paper we complete the proof of the existence of multiple solutions
(and, in particular, non minimal ones), to the epsilon-Dirichlet problem
obtained as a variational problem for the SU(2)-epsilon-Yang Mills functional.
This is equivalent to proving the existence of multiple solutions to the
Dirichlet problem for the SU(2)-Yang Mills functional with small boundary data.
In the first paper of this series this non-compact variational problem is
transformed into the finite dimensional problem of finding the critical points
of the function J(q), which is essentially the Yang Mills functional evaluated
on the approximate solutions, constructed via a gluing technique. In the
present paper, we establish a Morse theory for this function, by means of
Ljusternik-Schnirelmann theory, thus complete the proofs of the existence
theorems (Theorems 1-3).
