  Solutions of the stationary semilinear Cahn--Hilliard equation
  -\Delta^2 u - u -\Delta(|u|^{p-1}u)=0 in R^N, with p>1, which are
exponentially decaying at infinity, are studied. Using the Mounting Pass Lemma
allows us the determination of two different solutions. On the other hand, the
application of Lusternik--Schnirel'man (L--S) Category Theory shows the
existence of, at least, a countable family of solutions.
  However, through numerical methods it is shown that the whole set of
solutions, even in 1D, is much wider. This suggests that, actually, there
exists, at least, a countable set of countable families of solutions, in which
only the first one can be obtained by the L--S min-max approach.
