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Admissibility approach to nonuniform exponential dichotomies roughness with nonlocal perturbations

Jiawei He, Jianhua Huang

Abstract

Nonuniform exponential dichotomy serves as an important characteristic of nonuniform hyperbolicity, while admissibility of function classes is often used to characterize nonuniform exponential dichotomy. In this paper, we investigate the preservation of nonuniform exponential dichotomy under certain nonlocal perturbations. By utilizing the concept of admissibility of a pair of function classes, we establish sufficient conditions to ensure that the dichotomy results are consistent with those in the homogeneous situation. These results need to satisfy a smallness integrability condition.

Admissibility approach to nonuniform exponential dichotomies roughness with nonlocal perturbations

Abstract

Nonuniform exponential dichotomy serves as an important characteristic of nonuniform hyperbolicity, while admissibility of function classes is often used to characterize nonuniform exponential dichotomy. In this paper, we investigate the preservation of nonuniform exponential dichotomy under certain nonlocal perturbations. By utilizing the concept of admissibility of a pair of function classes, we establish sufficient conditions to ensure that the dichotomy results are consistent with those in the homogeneous situation. These results need to satisfy a smallness integrability condition.
Paper Structure (3 sections, 6 theorems, 75 equations)

This paper contains 3 sections, 6 theorems, 75 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The existence of nonuniform exponential dichotomies

Key Result

Lemma 3.1

Let for some appropriate $f\in X$, then $x$ is a solution of

Theorems & Definitions (14)

  • Definition 2.1
  • Definition 2.2
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • Theorem 3.1
  • proof
  • Lemma 3.4
  • ...and 4 more