A new approach to the problem of the equilibrium conditions of a self-interacting massive charged particles is presented. As is well-known, the solution of the Laplace or Poisson equation in a finite volume V, with or without charged particles inside, and with prescribed boundary conditions of the bounding surfaces, can be obtained by means of the Green's theorem and Green's functions. This solutions permits the choice of an arbitrary harmonic or potential functions inside the volume V. The generalized concept of the Green functions gives rise to the possibility that we can define these arbitrary harmonic or potential functions in order to generalize the well-known equilibrium conditions.