On two-dimensional systems of Volterra integral equations of the first kind

In this paper, we consider two-dimensional systems of Volterra integral equations of the first kind. The case where a system of integral equations of the second kind is obtained by differentiating the equations is well studied. We examine the case where this approach leads to a system of integral equations with an degenerate matrix of the principal part. We formulate sufficient conditions for the existence of a unique smooth solution in terms of matrix pencils.