Solutions for a class of neutral differential equations with nonatomicD-operator

This paper is concerned with the existence and uniqueness of solutions to first-order linear differential equations of neutral type with a nonatomicD-operator. We use an algebraic approach, in the context of the theory of convolution operators. Necessary and sufficient conditions are given for the initial value problem to have unique solutions for a class of equations.This work was done while the author was at the Department of Mathematics, Virginia Polytechnic Institute and State University.Instituto de Desarrollo Tecnológico para la Industria Quimica (INTEC), dependent on Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) and the Universidad Nacional del Litoral (UNL).