Abstract and Applied Analysis
Volume 2004 (2004), Issue 7, Pages 567-575
doi:10.1155/S1085337504306275

On linear singular functional-differential equations in a functional space

Abstract

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 ψ generating the space, one can guarantee resolubility and certain behavior of the solution near the point of singularity.