On Integral Equations the Kernels of Which are Homogeneous Functions of Degree (-1)

摘要

The present paper deals with integral equations the kernels of which are homogeneous functions of degree (-1). Factorization approach to such equations is developed. The constructed operator factorization is applied to the equation with a positive symmetric kernel. We prove that in the conservative case, both the homogeneous equation and the corresponding nonhomogeneous equation with a positive free term can possess positive solutions simultaneously.