Positive Fixed Points of Hammerstein Integral Operators with Degenerate Kernel - Yu. Kh. Eshkabilov; Sh. D. Nodirov (Учёные записки Казанского университета: Серия Физико-математические науки)
Positive ﬁxed points of the Hammerstein integral operators with a degenerate kernel in the space of continuous functions C [0, 1] were explored. The problem of determining the number of positive ﬁxed points of the Hammerstein integral operator was reduced to analyzing the positive roots of polynomials with real coeﬃcients. A model on a Cayley tree with nearestneighbor interactions and with the set [0, 1] of spin values was considered. It was proved that a unique translation-invariant Gibbs measure exists for this model.