Явные решения двумерного интегрального уравнения типа Вольтерра с граничной особой и сильно-особой линиями, когда корни характеристических уравнений вещественные, разные и равные

Abstract

The paper studies a two-dimensional integral equation of Volterra type with singular and strongly singular boundary lines. The solution of a two-dimensional integral equation of the Volterra type with singular kernels is sought in the class of continuous functions that vanish on the boundary lines. In the case when the roots of the characteristic equations are real, different and equal, the parameters of the equations are related to each other in a certain way, depending on the roots of the characteristic equations and the sign of the parameters of the integral equation, explicit solutions of the integral equation are found. It is proved that the solutions of a two-dimensional integral equation, depending on the sign of the parameters, can contain from one to four arbitrary continuous functions. The cases are determined when the solution to the integral equation is unique.