Abstract:
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.
Citation:
Kh. A. Khachatryan, “Positive solubility of some classes of non-linear integral equations
of Hammerstein type on the semi-axis and on the whole line”, Izv. Math., 79:2 (2015), 411–430
\Bibitem{Kha15}
\by Kh.~A.~Khachatryan
\paper Positive solubility of some classes of non-linear integral equations
of Hammerstein type on the semi-axis and on the whole line
\jour Izv. Math.
\yr 2015
\vol 79
\issue 2
\pages 411--430
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https://doi.org/10.1070/IM2015v079n02ABEH002748
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