Stable and Unstable Subspaces of a Critical Functional Differential Equation

摘要

The asymptotic behavior of a linear infinite delay, autonomous system of functional differential equations is studied. Conditions are found that ensure that a state space can be written as a direct sum of a stable subspace, characterized by the fact that solutions are small at infinity, a finite dimensional central subspace in which solutions are neither small nor large at infinity, and a finite dimensional exponentially unstable subspace consisting of exponentially growing solutions.