Special Session 28: Delay Differential Equations

In this work, we prove the existence of a center manifold for some partial functional differential equations, whose linear part is not necessarily densely defined but satisfies the Hille-Yosida condition. When the unstable space is reduced to zero, we also show the attractiveness of the center manifold. We prove that the flow on the center manifold is completely determined by an ordinary differential equation in a finite dimensional space. Finally, we prove that the stability of the equilibrium is completely determined by the stability of the flow on the center manifold in some critical cases.