Derivation and low density solution of a nonlinear Kirkwood-Salsburg equation

Nonlinear Kirkwood-Salsburg equations which are parametrized by the density ? are derived from the linear ones by elimination of the activity z. Upper bounds on ? are derived below which the solution of these equations is unique. Narrow upper and lower bounds on z(?) are obtained as well as upper bounds on the pair distribution function. Nonlinear Mayer-Montroll equations are also briefly discussed.