To the solution of one pseudo-Volterra integral equation

Abstract

In this paper, we study a homogeneous singular integral Volterra equation of the second kind (pseudo-Volterra integral equation). The singularity of the integral equation is shown. Properties of its kernel are proved. The characteristic equation is constructed. It is shown that it really is a characteristic equation for the studied integral equation. The kernel estimates of its integral operator are established. Solvability issues of the corresponding non-homogeneous integral equation are also researched. The weight class of the uniqueness for its solution is determined. A weight class is also established for the right side of the nonhomogeneous equation under study. The weight class of the uniqueness for its solution is defined on the basis of estimates for the kernel of the integral operator of the equation.