  We study a model based on $N$ scalar complex fields coupled to a scalar real
field, where all fields are treated classically as c-numbers. The model
describes a composite particle made up of $N$ constituents with bare mass $m_0$
interacting both with each other and with themselves via the exchange of a
particle of mass $\mu_0$. The stationary states of the composite particle are
described by relativistic Hartree's equations. Since the self-interaction is
included, the case of an elementary particle is a nontrivial special case of
this model. Using an integral transform method we derive the exact ground state
solution and prove its local stability. The mass of the composite particle is
calculated as the total energy in the rest frame. For the case of a massless
exchange particle the mass formula is given in closed form. The mass, as a
function of the coupling constant, possesses a well pronounced minimum for each
value of $\mu_0/m_0$, while the absolute minimum occurs at $\mu_0=0$.
