Positive fixed points of Hammerstein's integral operators with degenerate kernel

2019/11/25 by Eshkabilov Yusup Khalbaevich, Khalbaevich, Eshkabilov Yusup
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1911.10837

arxiv created 2019/11/25 · arxiv updated 2019/11/26

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.

Related

• On positive fixed points of operator of Hammerstein type with degenerate kernel and Gibbs Measures
• On positive solutions of the homogeneous Hammerstein integral equation
• Lyapunov operator \mathcal L with degenerate kernel and Gibbs measures
• Positive fixed points of cubic operators on ℝ² and Gibbs Measures
• Fixed points of Lyapunov integral operators and Gibbs measures