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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In the present work a generalized epidemic model containing a system of integral-differential equations is described. Using different transformations the system is reduced to a single nonlinear multidimensional integral equation. For the obtained equation the existence and uniqueness results are proved. Based on theoretical convergence results several application examples are presented with corresponding numerical results. [ABSTRACT FROM AUTHOR]