Positive Fixed Points of Hammerstein Integral Operators with Degenerate Kernel
https://doi.org/10.26907/2541-7746.2024.3.437-449
Abstract
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.
About the Authors
Yu. Kh. Eshkabilov
Tashkent International University of Financial Management and Technologies
Uzbekistan
Uzbekistan
Tashkent, 100025
Sh. D. Nodirov
Karshi State University
Uzbekistan
Uzbekistan
Karshi, 180119
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For citations:
Eshkabilov Yu.Kh., Nodirov Sh.D. Positive Fixed Points of Hammerstein Integral Operators with Degenerate Kernel. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2024;166(3):437-449. (In Russ.) https://doi.org/10.26907/2541-7746.2024.3.437-449
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