Explicitly Solution One Class Two Dimentional, Volterra Type Linear Integral Equation with Boundary Super-Singularity in Kernels

摘要

In this paper we found the solution of the two dimentional Volterra type linear Integral Equation with boundary super-singularity in kernels. In the first part of the paper, when function at present in kernels, connected between himself certain form, in depend from value signs numbers this functions in singular or super-singular point, the solution of Integral Equation will be found in explicit form. In the second part of this work will be considered the general case. In this case the problem finding of the solution considered Integral equation reduce to the problem finding of the solution of the Integral Equation type (1) in the case, when A(x) -B(y) = 0. In this case at specific condition to the functions present in kernels and on the right part, the problem finding the solution of this Integral Equation reduce to the problem of finding the solution of the one dimentional Volterra type system Integral Equations with super-singularity, the theory which investigated in works of N. Rajabov. In this foundation proved that the homogeneous Integral Equation have the infinity number of linear independent solutions.