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; email@example.com
F. H. Haydarov – National University of Uzbekistan, Tashkent, Uzbekistan; firstname.lastname@example.org
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.