Stability property and essential spectrum of linear retarded functional differential equations
The subject of this paper is the stability and stabilization of a class of delay functional differential equations in a Banach space. Using a family of Green operators, the solutions of the considered problem can be represented explicitly. The new notion of the retarded essential spectrum is introduced which generalizes the essential spectrum. As applications of the theoretical results, the case of heat equation is presented, in which the asymptotic stability is determined by the retarded point spectrum of the system, and the case of some Euler-Bernoulli beam equations with time delay.
Euler-Bernoulli beam equation with time delay
scientific article; zbMATH DE number 6138044