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Transactions of the Moscow Mathematical Society

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On positive solutions of one class of nonlinear integral equations of Hammerstein-Nemytskiĭ type on the whole axis


Author: Kh. A. Khachatryan
Translated by: E. Khukhro
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 75 (2014), vypusk 1.
Journal: Trans. Moscow Math. Soc. 2014, 1-12
MSC (2010): Primary 45GXX
DOI: https://doi.org/10.1090/S0077-1554-2014-00226-0
Published electronically: November 4, 2014
MathSciNet review: 3308598
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Abstract: This paper is devoted to studying one class of nonlinear integral equations of Hammerstein-Nemytskiĭ type on the whole axis, which occurs in the theory of transfer in inhomogeneous medium. It is proved that these equations can be solved in various function spaces, and the asymptotic behaviour at infinity of the solutions that are constructed is studied.


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Additional Information

Kh. A. Khachatryan
Affiliation: Institute of Mathematics of National Academy of Sciences of Armenia
Email: Khach82@rambler.ru, Khach82@mail.ru

DOI: https://doi.org/10.1090/S0077-1554-2014-00226-0
Keywords: Positive solution, Carath\'eodory condition, convergence of iterations, monotonicity, inhomogeneous medium, Hammerstein--Nemytski\u{\i} equation
Published electronically: November 4, 2014
Article copyright: © Copyright 2014 Kh.A. Khachatryan