Geodesic
Positive solubility of some classes of non-linear integral equations
Izvestiya. Mathematics , Tome 79 (2015) no. 2, pp. 411-430

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We study certain classes of non-linear Hammerstein integral equations on the semi-axis and the whole line. These classes of equations arise in the theory of radiative transfer in nuclear reactors, in the kinetic theory of gases, and for travelling waves in non-linear Richer competition systems. By combining special iteration methods with the methods of construction of invariant cone segments for the appropriate non-linear operator, we are able to prove constructive existence theorems for positive solutions in various function spaces. We give illustrative examples of equations satisfying all the hypotheses of our theorems.
Keywords: Hammerstein equation, Carathéodory condition, monotonicity, induction, iterations
Mots-clés : convergence. 
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     author = {Kh. A. Khachatryan},
     title = {Positive solubility of some classes of non-linear integral equations},
     journal = {Izvestiya. Mathematics },
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     url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_2_a8/}
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Kh. A. Khachatryan. Positive solubility of some classes of non-linear integral equations. Izvestiya. Mathematics , Tome 79 (2015) no. 2, pp. 411-430. http://geodesic.mathdoc.fr/item/IM2_2015_79_2_a8/