Article

Positive Fixed Points of Hammerstein Integral Operators with Degenerate Kernel

Yu. Kh. ÈshkabilovTashkent International University of Financial Management and TechnologiesSh. D. NodirovKarshi State University

Učenye zapiski Kazanskogo gosudarstvennogo universiteta. Seriâ Fiziko-matematičeskie nauki/Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie naukijournal2024en

ABI

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.

Topics

Numerical methods in inverse problems Differential Equations and Boundary Problems Approximation Theory and Sequence Spaces

Identifiers

DOI: 10.26907/2541-7746.2024.3.437-449

Citations and references

Cited by 1 18 references

Metrics — AkademScholar · Coming soon