We use a special space of integrable functions for studying the Cauchy problem for linear functional-differential equations with nonintegrable singularities. We use the ideas developed by Azbelev and his students (1995). We show that by choosing the function generating the space, one can guarantee resolubility and certain behavior of the solution near the point of singularity.
"On linear singular functional-differential equations in one functional space." Abstr. Appl. Anal. 2004 (7) 567 - 575, 29 June 2004. https://doi.org/10.1155/S1085337504306275