Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Amerio's Theorem for Remotely Almost Periodic Differential Equations

David Cheban

Abstract

The aim of this paper is to study the remotely almost periodic motions of dynamical systems and solutions of nonlinear differential equations. We establish some properties of remotely almost periodic motions and generalize the well known Amerio's theorem for abstract remotely almost periodic dynamical systems. Application of our general results for different classes of nonlinear differential/difference and algebraic equations is given.

Amerio's Theorem for Remotely Almost Periodic Differential Equations

Abstract

The aim of this paper is to study the remotely almost periodic motions of dynamical systems and solutions of nonlinear differential equations. We establish some properties of remotely almost periodic motions and generalize the well known Amerio's theorem for abstract remotely almost periodic dynamical systems. Application of our general results for different classes of nonlinear differential/difference and algebraic equations is given.

Paper Structure

This paper contains 15 sections, 69 theorems, 165 equations.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Amerio's Theorem for Nonautonomous Dynamical Systems and Their Generalizations
  4. Amerio's theorem for remotely almost periodic NDS
  5. Remotely Almost Periodic NDSs with Positively Uniformly Asymptotically Stable Trajectories
  6. Applications
  7. Ordinary differential equations
  8. Difference equations
  9. Functional differential equations with finite delay
  10. Ordinary Stochastic Differential Equations
  11. Algebraic equations
  12. Funding
  13. Data availability
  14. Conflict of Interest
  15. ORCID ID

Key Result

Theorem 1.6

(Amerio's theorem) Let $Q$ be a compact subset of the Banach space $\mathfrak B$. Assume that the following conditions are fulfilled: Then the solution $\varphi$ is almost periodic.

Theorems & Definitions (169)

  • Definition 1.1
  • Definition 1.2
  • Remark 1.3
  • Definition 1.4
  • Definition 1.5
  • Theorem 1.6
  • Remark 1.7
  • Theorem 1.8
  • Definition 1.9
  • Definition 1.10
  • ...and 159 more