  Originally, the SW-equations discovered by Seiberg-Witten are 1st-order PDE,
which solutions (A,\phi), with \phi\ne 0, are known as SW-monopoles. It is
known that the solutions of these 1st-order eq correspond to the minimum of
  SW-functional. However, it is not true, that for all spin^{c} class \alpha,
the minimum is always attained by this sort of solution. In fact, there are
only a finite number of \alpha such that the minimum is a SW-monopole. We show
a necessary condition to be satisfied by the class \alpha in order to the
minimum be a SW-monopole.
