Remotely Almost Periodic Solutions of Scalar Differential Equations

2025/10/01 by Cheban, David
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.00474

Abstract

The aim of this paper is to study the problem of existence of remotely almost periodic solutions for the scalar differential equation x'=f(t,x), where f:\mathbb R× \mathbb R→ \mathbb R is a continuous, monotone in x and remotely almost periodic in t function. We prove that every solution φ of this equation bounded on the semi-axis \mathbb R₊ is remotely almost periodic. This statement is a generalization of the well-known Opial's theorem for remotely almost periodic scalar differential equations. We also establish a similar statement for scalar difference equations.

Citations

• Massera's theorem for Asymptotically Periodic Scalar Differential Equations

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