NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2015, 6 (5), P. 618–627
On positive solutions of the homogeneous Hammerstein integral equation
Yu. Kh. Eshkabilov – National University of Uzbekistan, Tashkent, Uzbekistan; yusup62@mail.ru
F. H. Haydarov – National University of Uzbekistan, Tashkent, Uzbekistan; haydarov_imc@mail.ru
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
DOI 10.17586/2220-8054-2015-6-5-618-627