We study a class of two-dimensional integral equations in the plane with monotonic nonlinearity. These equations have numerous applications in many various fields of natural science. Thus, equations of this kind appear in the dynamic theory of p-adic open-closed strings, in the mathematical theory of space-and-time spread of epidemics, in the kinetic theory of gases (the Boltzmann kinetic equation within the framework of various models), and 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 the obtained results have applications in the theory of p-adic open-closed strings and in the mathematical biology. The methods used to prove 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 application of these equations illustrating the accumulated results.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 5, pp. 695–711, May, 2021. Ukrainian DOI: 10.37863/umzh.v73i5.6541.
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Khachatryan, K.A., Petrosyan, H.S. On Bounded Solutions of a Class of Nonlinear Integral Equations in the Plane and the Urysohn Equation in a Quadrant of the Plane. Ukr Math J 73, 811–829 (2021). https://doi.org/10.1007/s11253-021-01961-8
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DOI: https://doi.org/10.1007/s11253-021-01961-8