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Exponential Ordering for Nonautonomous Neutral Functional Differential Equations

Sylvia Novo, Rafael Obaya, Víctor M. Villarragut

TL;DR

It is shown that the omega-limit sets are copies of the base to explain the long-term behavior of the trajectories of monotone skew-product semiflows generated by families of nonautonomous neutral functional differential equations with infinite delay and stable D-operator.

Abstract

We study monotone skew-product semiflows generated by families of nonautonomous neutral functional differential equations with infinite delay and stable D-operator, when the exponential ordering is considered. Under adequate hypotheses of stability for the order on bounded sets, we show that the omega-limit sets are copies of the base to explain the long-term behavior of the trajectories. The application to the study of the amount of material within the compartments of a neutral compartmental system with infinite delay, shows the improvement with respect to the standard ordering.

Exponential Ordering for Nonautonomous Neutral Functional Differential Equations

TL;DR

It is shown that the omega-limit sets are copies of the base to explain the long-term behavior of the trajectories of monotone skew-product semiflows generated by families of nonautonomous neutral functional differential equations with infinite delay and stable D-operator.

Abstract

We study monotone skew-product semiflows generated by families of nonautonomous neutral functional differential equations with infinite delay and stable D-operator, when the exponential ordering is considered. Under adequate hypotheses of stability for the order on bounded sets, we show that the omega-limit sets are copies of the base to explain the long-term behavior of the trajectories. The application to the study of the amount of material within the compartments of a neutral compartmental system with infinite delay, shows the improvement with respect to the standard ordering.
Paper Structure (6 sections, 13 theorems, 118 equations)

This paper contains 6 sections, 13 theorems, 118 equations.

Table of Contents

  1. Introduction
  2. Some preliminaries
  3. Exponential ordering
  4. Stability of omega-limit sets
  5. Topological structure of omega-limit sets
  6. Applications to compartmental systems

Key Result

Proposition 3.1

\newlabelestableabierto Let us assume that $D$ satisfies (D1)-(D4) and it is given by Dformula. Then, there is an $\varepsilon>0$ such that for any $\nu^*=[\nu^*_{ij}]$ where $\nu^*_{ij}$ is a real regular Borel measure with finite total variation, $|\nu^*_{ij}|(\{0\})=0$ for each $i$, $j\in{1,\ldo is stable.

Theorems & Definitions (28)

  • Proposition 3.1
  • proof
  • Proposition 3.2
  • proof
  • Theorem 3.5
  • proof
  • Definition 4.1
  • Definition 4.2
  • Definition 4.3
  • Proposition 4.4
  • ...and 18 more