We study one class of nonlinear integral equations of convolution type with the Hammerstein–Nemytskii operator on the whole axis. This class has direct applications in the kinetic theory of gases, the theory of p-adic open-closed strings, and the theory of radiative transfer. We prove a constructive theorem on the existence of a nontrivial nonnegative solution integrable on the whole axis. In the end of the paper, we give specific examples of such equations satisfying all conditions of the main theorem.
Keywords: Hammerstein–Nemytskii equations, successive approximations, monotonicity, convexity, convergence of iterations.
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Received November 18, 2019
Revised January 22, 2020
Accepted January 27, 2020
Funding Agency: The study was funded by a grant from the Russian Science Foundation (project № 19-11-00223).
Khachatur Aghavardovich Khachatryan, Dr. Phys.-Math. Sci., Institute of Mathematics, National Academy of Sciences of Armenia, 0019, Yerevan, Republic of Armenia; Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, 119991 Russia,
e-mail: Khach82@rambler.ru.
Haykanush Samvelovna Petrosyan, Cand. Sci. (Phys.-Math.), Armenian National Agrarian University, 0009, Yerevan, Republic of Armenia; Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, 119991 Russia, e-mail: Haykuhi25@mail.ru.
Cite this article as: Kh.A.Khachatryan, H.S.Petrosyan. On the construction of an integrable solution to one class of nonlinear integral equations of Hammerstein–Nemytskii type on the whole axis. Trudy Instituta Matematiki i Mekhaniki URO RAN, 2020, vol. 26, no. 2, pp. 278–287.
