  Exact multicentered solutions to the governing equations of the Born--Infeld
nonlinear theory of electrodynamics describing distributions of electric,
magnetic, and dyonic point charge sources are constructed explicitly for the
first time. The method of construction may effectively be adapted to obtain
such solutions in generalized theories as well. As a consequence, the solutions
unveil that, in order to achieve a balance between such multicentered electric
or magnetic point charge distribution in equilibrium, a static magnetic or
electric current must be present, resulting in non-conservativeness of the
induced electric or magnetic intensity field, respectively and universally.
Moreover, it is also shown that the methods of construction and conclusions
drawn in the multicentered situation may be extended to obtain exact solutions
and similar conclusions, explicitly, in the situation of continuously
distributed charge source problems.
