Memoirs of the American Mathematical Society 2009; 71 pp; softcover Volume: 202 ISBN10: 0821846531 ISBN13: 9780821846537 List Price: US$66 Individual Members: US$39.60 Institutional Members: US$52.80 Order Code: MEMO/202/951
 Several types of differential equations, such as delay differential equations, agestructure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with nondense domain. Using LiapunovPerron method and following the techniques of Vanderbauwhede et al. in treating infinite dimensional systems, the authors study the existence and smoothness of center manifolds for semilinear Cauchy problems with nondense domain. As an application, they use the center manifold theorem to establish a Hopf bifurcation theorem for age structured models. Table of Contents  Introduction
 Integrated semigroups
 Spectral decomposition of the state space
 Center manifold theory
 Hopf bifurcation in age structured models
 Bibliography
