Questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole line

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Abstract

We consider a class of nonlinear integral equations with a stochastic and symmetric kernel on the whole line. With certain particular representations of the kernel and nonlinearity, equations of the mentioned type arise in many branches of mathematical natural science. In particular, such equations occur in the theory p-adic strings, in the kinetic theory of gases, in mathematical biology and in the theory of radiative transfer. Constructive existence theorems are proved for non-negative non-trivial and bounded solutions under various restrictions on the function describing the nonlinearity in the equation. Under additional restrictions on the kernel and on the nonlinearity, a uniqueness theorem is also proved in a certain class of bounded and non-negative functions that have a finite limit in ±∞. At the end, specific applied examples of the kernel and non-linearity are given that satisfy to all restrictions of the proven statements.

About the authors

Khachatur A. Khachatryan

Yerevan State University;
Lomonosov Moscow State University

Author for correspondence.
Email: khachatur.khachatryan@ysu.am
ORCID iD: 0000-0002-4835-943X
SPIN-code: 6783-9479
Scopus Author ID: 24461615400
http://www.mathnet.ru/person27540

D.Sc. (Phys. & Math. Sci.), Professor; Head of the Dept.; Dept. of Theory of Functions and Differential Equations1; Leading Member of the grant of the Russian Science Foundation (project no. 19–11–00223)3

1, A. Manukyan str., Yerevan, 0025, Armenia; 1, Leninskie Gory, Moscow, 119991, Russian Federation

Haykanush S. Petrosyan

Armenian National Agrarian University;
Lomonosov Moscow State University

Email: haykuhi25@mail.ru
ORCID iD: 0000-0002-7172-4730
Scopus Author ID: 57201727643
http://www.mathnet.ru/person85670

Cand. Phys. & Math. Sci., Associate Professor; Dept of Higher Mathematics and Physics2; Member of the grant of the Russian Science Foundation (project no. 19–11–00223)3

1, A. Manukyan str., Yerevan, 0025, Armenia; 1, Leninskie Gory, Moscow, 119991, Russian Federation

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