In the theory of Gibbs measures there are a lot of papers which devoted to Gibbs measures on a Cayley tree [1]. Translation-invariant Gibbs measures for models with a ontinuum set of spin values is reduced to find positive fixed points of nonlinear integral operators Hammerstein’s type [2]. In [3],[4] proven theorems, that integral operators Hammerstein’s type can have one, two and three positive fixed points.