Geodesic
On solution of a class of Hammerstein type nonlinear integral equations on the positive half-line in the critical case
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2014), pp. 31-39

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In the this article a class of nonlinear integral equations with noncompact Hammerstein integral operator, the kernel of which depends on difference of its arguments is investigated. Above mentioned class of equations arises in the kinetic theory of gases and in the radiative transfer theory in nuclear reaction. Combination of special iteration methods with the methods of the theory of construction of invariant cone-shaped segments allow to prove existence theorems of positive solutions in special selected weighted space.
Keywords: Hammerstein type equation, completely monotone kernel, iteration, Caratheodory’s condition
Mots-clés : monotony, convergence. 
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     title = {On solution of a class of {Hammerstein} type nonlinear integral equations on the positive half-line in the critical case},
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H. S. Petrosyan. On solution of a class of Hammerstein type nonlinear integral equations on the positive half-line in the critical case. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2014), pp. 31-39. http://geodesic.mathdoc.fr/item/UZERU_2014_3_a5/