The Existence and Application of Unbounded Connected Components

Abstract EN

Let X be a Banach space and Cn a family of connected subsets of R×X.

We prove the existence of unbounded components in superior limit of {Cn}, denoted by lim¯ Cn, which have prescribed shapes.

As applications, we investigate the global behavior of the set of positive periodic solutions to nonlinear first-order differential equations with delay, which can be used for modeling physiological processes.