On positive solutions of the homogeneous Hammerstein integral equation

Yu. Kh. Eshkabilov, F. H. Haydarov

National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: In this paper the existence and uniqueness of positive fixed points operator for a nonlinear integral operator are discussed. We prove the existence of a finite number of positive solutions for the Hammerstein type of integral equation. Obtained results are applied to the study of Gibbs measures for models on a Cayley tree.

Keywords: integral equation of Hammerstein type, fixed point of operator, Gibbs measure, Cayley tree.

PACS: 02.30.Rz

Received: 02.04.2015
Revised: 18.07.2015

Language: English

DOI: 10.17586/2220-8054-2015-6-5-618-627

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