Asymptotic Behavior of the Solution for One Class of Nonlinear Integral Equations of Hammerstein Type on the Whole Axis
- Authors: Khachatryan K.A.1,2, Petrosyan H.S.3,2
-
Affiliations:
- Yerevan State University
- Lomonosov Moscow State University
- National Agrarian University of Armenia
- Issue: Vol 68, No 2 (2022)
- Pages: 376-391
- Section: Articles
- URL: https://journals.rudn.ru/CMFD/article/view/31161
- DOI: https://doi.org/10.22363/2413-3639-2022-68-2-376-391
Cite item
Full Text
Abstract
A class of nonlinear integral equations on the whole axis with a noncompact integral operator of Hammerstein type is investigated. This class of equations has applications in various fields of natural science. In particular, such equations are found in mathematical biology, in the kinetic theory of gases, in the theory of radiation transfer, etc. The existence of a nonnegative nontrivial and bounded solution is proved. The asymptotic behavior of the constructed solution on ±∞ is studied. In one important special case, the uniqueness of the constructed solution in a certain weighted space is established. At the end of the work, specific applied examples of the equations under study are given.
About the authors
Kh. A. Khachatryan
Yerevan State University; Lomonosov Moscow State University
Email: khachatur.khachatryan@ysu.am
Yerevan, Armenia; Moscow, Russia
H. S. Petrosyan
National Agrarian University of Armenia; Lomonosov Moscow State University
Author for correspondence.
Email: Haykuhi25@mail.ru
Yerevan, Armenia; Moscow, Russia
References
- Владимиров В.С., Волович Я.И. О нелинейном уравнении динамики в теории p-адической струны// Теор. мат. физ. -2004.-138, № 3.-С. 355-368.
- Енгибарян Н.Б. Об одной задаче нелинейного переноса излучения// Астрофизика.- 1966.- 2, № 1.- С. 31-36.
- Жуковская Л.В. Итерационный метод решения нелинейных интегральных уравнений, описывающих роллинговые решения в теории струн// Теор. мат. физ.-2006.- 146, № 3.- С. 402-409.
- Колмогоров А.Н., Фомин С.В. Элементы теории функций и функционального анализа.- М.: Наука, 1976.
- Хачатрян А.Х., Хачатрян Х.А., Петросян А.С. Асимптотическое поведение решения для одного класса нелинейных интегро-дифференциальных уравнений в задаче распределения дохода// Тр. Инта мат. и мех. УрО РАН. -2021.-27, № 1.- С. 188-206.
- Хачатрян Х.А. О разрешимости некоторых классов нелинейных интегральных уравнений в теории p-адической струны// Изв. РАН. Сер. мат.-2018.- 82, № 2. -С. 172-193.
- Arabadzhyan L.G. Solutions of certain integral equations of the Hammerstein type// J. Contemp. Math. Anal. -1997.-32, № 1.- С. 17-24.
- Arabadzhyan L.G., Khachatryan A.S. A class of integral equations of convolution type// Sb. Math.- 2007.-198, № 7.-С. 949-966.
- Barbour A.D. The uniqueness of Atkinson and Reuter’s epidemic waves// Math. Proc. Cambridge Phil. Soc. -1977.- 82, № 1.- C. 127-130.
- Cercignani C. The Boltzmann Equation and Applications. -New York: Springer, 1988.
- Diekmann O. Thresholds and travelling waves for the geographical spread of infection// J. Math. Biol.- 1978.-6, № 2.-С. 109-130.
- Khachatryan A.Kh., Khachatryan Kh.A. Solvability of a nonlinear model Boltzmann equation in the problem of a plane shock wave// Theoret. and Math. Phys.- 2016.- 189, № 2.- С. 1609-1623.
- Khachatryan A.Kh., Khachatryan Kh.A. On the solvability of some nonlinear integral equations in problems of epidemic spread// Proc. Steklov Inst. Math.- 2019.- 306.- C. 271-287.
- Khachatryan Kh.A. Positive solubility of some classes of non-linear integral equations of Hammerstein type on the semi-axis and on the whole line// Izv. Math.- 2015.- 79, № 2.-С. 411-430.
- Khachatryan Kh.A., Petrosyan H.S. On the solvability of a class of nonlinear Hammerstein-Stieltjes integral equations on the whole line// Proc. Steklov Inst. Math. -2020.-308.-С. 238-249.
- Khachatryan Kh.A., Petrosyan H.S. Some integral equations on the whole line with monotone nonlinearity and a difference kernel// J. Math. Sci. (N.Y.). - 2021.- 255, № 6.- С. 790-804.
