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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Kazan Federal University
2024-10-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
| Subjects: | |
| 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. |
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| ISSN: | 2541-7746 2500-2198 |