A general class of autoconvolution equations of the third kind

Continuing recent investigations by L. Berg and L. v. Wolfersdorf on a model integral equation of autoconvolution type of the third kind, two existence theorems for a general class of such equations axe derived. Further, an existence theorem is proved for the model equation with data and solutions of a general logarithmic form. Moreover, a singular perturbation problem for a related integrodifferential equation of first order to the model equation is studied which could serve as a basis for its regularization by the Lavrentiev method.