Positive Fixed Points of Hammerstein Integral Operators with Degenerate Kernel

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 polynomia...

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Bibliographic Details
Main Authors: Yu. Kh. Eshkabilov, Sh. D. Nodirov
Format: Article
Language:English
Published: Kazan Federal University 2024-10-01
Series:Учёные записки Казанского университета: Серия Физико-математические науки
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Online Access:https://uzakufismat.elpub.ru/jour/article/view/102
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Summary: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.
ISSN:2541-7746
2500-2198