  From \cite{re} From \cite{re} it is known that ``translation-invariant Gibbs
measures" of the model with an uncountable set of spin values can be described
by positive fixed points of a nonlinear integral operator of Hammerstein type.
In \cite{enh2015, MSSX} there are main results on positive fixed points of the
operator of Hammerstein type with degenerate kernels, but it was not solved the
existence of Gibbs measures corresponding to the founded fixed points for
constructed kernels. This paper is an investigation of the papers
\cite{enh2015} and \cite{MSSX}. In this paper we construct new degenerate
kernels of the Hammerstein operator by taking into account problems in the
theory of Gibbs measure, i.e. each positive fixed point of the operator gives
translational-invariant Gibbs measure.
