  We consider models with nearest-neighbor interactions and with the set
$[0,1]$ of spin values, on a Cayley tree of order $k\geq 1$.
  It is known that the "splitting Gibbs measures" of the model can be described
by solutions of a nonlinear integral equation. Recently, solving this integral
equation some periodic (in particular translation-invariant) splitting Gibbs
measures were found. In this paper we give three constructions of new sets of
non-translation-invariant splitting Gibbs measures. Our constructions are based
on known solutions of the integral equation.
