Solutions of the Yvon–Born–Green and Kirkwood equations for hard spheres at very high densities

The Yvon–Born–Green and Kirkwood equations with superposition approximation for g(2)(x) for a system of hard spheres are found to have multiple solutions over broad ranges of density. These solutions are related to those of an earlier study of high density solutions to the Yvon–Born–Green equation for hard spheres. The extension of these findings to systems of square-well molecules is discussed. The results of the study are interpreted in the framework of a bifurcation theoretical analysis of the problem.