Amerio's Theorem for Remotely Almost Periodic Differential Equations

TL;DR

This paper extends Amerio's theorem to analyze remotely almost periodic solutions in nonlinear differential equations, providing new theoretical insights and applications across various classes of equations.

Contribution

It generalizes Amerio's theorem to remotely almost periodic motions, broadening its applicability to nonlinear differential, difference, and algebraic equations.

Findings

Established properties of remotely almost periodic motions

Generalized Amerio's theorem for abstract systems

Applied results to various nonlinear 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.