  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. For arbitrary $k\geq 2$ we find
a sufficient condition under which the integral equation has unique solution,
hence under the condition the corresponding model has unique splitting Gibbs
measure.
