Persistence in non-autonomous quasimonotone parabolic partial functional differential equations with delay

Abstract

<p style='text-indent:20px;'>This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type Ⅱ over a minimal set are given. Then, practical criteria for the uniform or strict persistence of the systems above a minimal set are obtained.