Autoconvolution equations of the third kind with power-logarithmic coefficients

Abstract

Existence and uniqueness theorems for a basic class of autoconvolution equations of the third kind with power-logarithmic coefficeint and free term are derived. Under suitable assumptions the existence of a solitary solution and of a one-parametric family of solutions is proved.

Keywords:

• quadratic integral equations
• autoconvolution equations
• linear singular Volterra equations

AMS Subject Classifications:

• 45D05
• 45E10