A semigroup theory for a differential equation with delayed and advanced arguments is developed, with a detailed description of the infinitesimal generator. This in turn allows to study the exact controllability of the equation, by rewriting it as a classical Cauchy problem.
Raúl Manzanilla. Luis Gerardo Mármol. Carmen J. Vanegas. "On the Controllability of a Differential Equation with Delayed and Advanced Arguments." Abstr. Appl. Anal. 2010 1 - 16, 2010. https://doi.org/10.1155/2010/307409