  In this paper we consider a model with nearest-neighbor interactions and with
the set $[0,1]$ of spin values, on a Cayley tree of order $k \geq 2$. To study
translation-invariant Gibbs measures of the model we drive an nonlinear
functional equation. For $k=2$ and 3 under some conditions on parameters of the
model we prove non-uniqueness of translation-invariant Gibbs measures (i.e.
there are phase transitions).
