Abstract
This article attends to the specific inverse problem of determining the difference kernel k of a second kind linear Volterra integral equation of convolution type from a prescribed quotient μ of resolvent r and kernel k of the equation. A problem of this type arises, for example, in the theory of viscoelasticity and leads to a nonlinear integral equation of the third kind , for which several existence theorems are proved. Moreover, the applicability of Tikhonov's regularization method is studied. Finally, the case of non-convolution Volterra equations is also briefly discussed.