Geodesic
On positive solutions of the homogeneous Hammerstein integral equation
Nanosistemy: fizika, himiâ, matematika, Tome 6 (2015) no. 5, pp. 618-627

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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. 
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     author = {Yu. Kh. Eshkabilov and F. H. Haydarov},
     title = {On positive solutions of the homogeneous {Hammerstein} integral equation},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {618--627},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2015_6_5_a1/}
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Yu. Kh. Eshkabilov; F. H. Haydarov. On positive solutions of the homogeneous Hammerstein integral equation. Nanosistemy: fizika, himiâ, matematika, Tome 6 (2015) no. 5, pp. 618-627. http://geodesic.mathdoc.fr/item/NANO_2015_6_5_a1/