Volterra's equation of the second kind with incompressible kernel

Abstract

In the article the singular Volterra's integral equation of the second kind is considered, which because of the incompressible of the kernel classical methods of solutions are not applicable. It is shown that the corresponding homogeneous equation at vertical bar lambda vertical bar > 1 has a continuous spectrum, and the multiplicity of the characteristic numbers grows with increasing vertical bar lambda vertical bar. By the Carleman-Vekua method the equation is reduced to Abelequation. The eigenfunctions of the equation are found in an explicit form.