Representation of solutions and stability of linear differential-difference equations in a Banach space

AbstractIn this paper the theory of linear delay differential equations is extended in three directions. One, the underlying phase space is allowed to be a Banach space so that equations with unbounded operators may be considered. Two, the delay is permitted to be effective over an infinite interval and a connection is made between this type of system and neutral systems whose delay is effective over a finite interval. Three, a theory of uniform asymptotic stability for linear delay differential equations in a Hilbert space is developed