Functional Differential Equations

Abstract

The goal of this chapter is to apply the theories developed in the previous chapters to functional differential equations. In Section 7.1 retarded functional differential equations are rewritten as abstract Cauchy problems and the integrated semigroup theory is used to study the existence of integrated solutions and to establish a general Hopf bifurcation theorem. Section 7.2 deals with neutral functional differential equations. In Section 7.3, firstly it is shown that a delayed transport equation for cell growth and division has asynchronous exponential growth; secondly it is demonstrated that partial functional differential equations can also be set up as abstract Cauchy problems.