  We use the SU(2) 't Hooft-Polyakov monopole configuration, and its BPS
version, to test the integral equations of the Yang-Mills theory. Those
integral equations involve two (complex) parameters which do not appear in the
differential Yang-Mills equations, and if they are considered to be arbitrary
it then implies that non-abelian gauge theories (but not abelian ones) possess
an infinity of integral equations. For static monopole configurations only one
of those parameters is relevant. We expand the integral Yang-Mills equation in
a power series of that parameter and show that the 't Hooft-Polyakov monopole
and its BPS version satisfy the integral equations obtained in first and second
order of that expansion. Our results points to the importance of exploring the
physical consequences of such an infinity of integral equations on the global
properties of the Yang-Mills theory.
