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A class of nonlinear singular integral equations on the whole line is considered. This class of equations for specific representations of nonlinearity and kernel arises in dynamic theory of p-adic strings, in mathematical theory of the pandemic spread within the framework of modified Diekmann-Kapper model, in the theory of radiative transfer in nonhomogeneous medium and kinetic theory of gases. In this paper we will investigate and reveal new qualitative properties of the solution of the above mentioned equations. Relying on these properties as well as some geometric inequalities for convex downward functions we will prove the uniqueness of the solution in the class of bounded functions whose infimum is a positive number. At the end we will present examples of such equations, satisfying all restrictions of the proven statements., Author(s): A.Kh. Khachatryan [sup.1], Kh.A. Khachatryan [sup.2] Author Affiliations: (1) https://ror.org/05xvhyj32, grid.449095.5, 0000 0004 0482 6758, Armenian National Agrarian University, , 74 Teryan St., 0009, Yerevan, Armenia (2) https://ror.org/00s8vne50, grid.21072.36, [...]

The paper studies the issues of existence, absence and uniqueness of nontrivial nonnegative and bounded solution for one class of nonlinear integral equations on the whole line with symmetric and positive kernel. In the class of integral equations under study, the nonlinearity is a monotonic and convex function on the positive part of the real axis. The above mentioned class of integral equations, with various particular representations of the kernel and nonlinearity, has applications in many areas of mathematical physics and mathematical biology. At the end of the work particular examples of kernel and nonlinearity satisfying all conditions of the proved statements are given., Author(s): Kh.A. Khachatryan [sup.1] [sup.2], H.S. Petrosyan [sup.2] [sup.3], A. R. Hakobyan [sup.4] Author Affiliations: (1) https://ror.org/00s8vne50, grid.21072.36, 0000 0004 0640 687X, Yerevan State University, , Alex Manoogian St., 0025, [...]

We investigate qualitative properties of solutions of special classes of convolution type nonlinear integral equations on the whole line. We study the asymptotic properties, continuity, and monotonicity of arbitrary nontrivial bounded solutions. Depending on the properties of the kernel of the equation, we find out whether there exist nontrivial bounded solutions with a finite limit at [+ or -]00. Based on the obtained results, we establish uniqueness theorems for large classes of bounded functions. The results obtained are illustrated by examples from applications. Bibliography: 7 titles. Illustrations: 3 figures., 1 Introduction The paper is devoted to the study of convolution type nonlinear integral equations [Please download the PDF to view the mathematical expression] (1.1) for a continuous bounded function [...]

We prove the existence of a rolling odd solution to a boundary value problem for a convolution type nonlinear singular integral equation on the whole axis with power non-linearity. We obtain the integral asymptotic formula for the solution and describe some examples. Bibliography: 12 titles., Introduction We consider the boundary value problem for a singularly nonlinear integral equation on the axis [Please download the PDF to view the mathematical expression], (1) [Please download the PDF [...]