Positive fixed points of Hammerstein's integral operators with degenerate kernel
Functional Analysis
2019-11-26 v1
Abstract
In this paper we study positive fixed points of Hammerstein integral operators with degenerate kernel in the cone of C[0, 1]. Problem on a number of positive fixed points of the Hammerstein integral operator leads to the study positive roots of polynomials with real coefficients. Consider a model on a Cayley tree with nearest-neighbor interactions and with the set [0, 1] of spin values. The uniqueness translational-invariant Gibbs measures for the given model is proved.
Keywords
Cite
@article{arxiv.1911.10837,
title = {Positive fixed points of Hammerstein's integral operators with degenerate kernel},
author = {Eshkabilov Yusup Khalbaevich},
journal= {arXiv preprint arXiv:1911.10837},
year = {2019}
}