On bounded solutions of a class of nonlinear integral equations on the plane and the Urysohn equation in a quadrant of the plane
Abstract
UDC 517.968.4
We study a class of two-dimensional integral equations in the plane with monotonic nonlinearity.
These equations have a lot of applications in many fields of natural science.
For example, such equations arise in the dynamic theory of $p$-adic open-closed strings, in the mathematical theory of spatio-temporal spread of epidemics, in the kinetic theory of gases (the Boltzmann kinetic equation in the framework of various models), in the theory of radiative transfer.
We prove a constructive existence theorem for bounded nontrivial solutions and for solutions with alternating sign.
It is shown that obtained results have applications in the theory of $p$-adic open-closed strings and in mathematical biology.
The methods used in the proof of the theorem make it possible to investigate a class of two-dimensional integral equations of the Urysohn type in a quadrant of the plane.
At the end of the paper, we provide specific examples of applications of these equations to illustrate the obtained results.
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