Nontranslation invariant Gibbs measures for models with uncountable set of spin values on a Cayley tree

We consider models with nearest-neighbour interactions and with the set [0, 1] of spin values, on a Cayley tree of order k ≥ 1. It is known that the “splitting Gibbs measures” of the model can be described by solutions of a nonlinear integral equation. Recently, by 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 nontranslation invariant splitting Gibbs measures. Our constructions are based on known solutions of the integral equation (1.5).