Poisson Stable Solutions and Their Exponential Attractiveness for Difference Equations

Axioms 2026 Open access

Read full text
Authors: Huasong Xiao, Junfei Cao, Bing He
DOI: 10.3390/axioms15010073
Cited by: 0

Abstract

We consider the Poisson stable solutions and their exponential attractiveness for the linear difference equation z(n+1)=Az(n)+g(n) and semi-linear difference equation z(n+1)=Az(n)+G(n,z(n)). Via Shcherbakov’s comparability principle, we show that if the forcing g (respectively, G) has some Poisson stable property, there is precisely one bounded solution that shares the same recurrence character as g(respectively, G) under appropriate assumptions. Moreover, the unique Poisson stable solution exponentially attracts every other solution.

Fields of Study & Subjects

Nonlinear Differential Equations Analysis Mathematical Dynamics and Fractals Advanced Differential Equations and Dynamical Systems

Publication details

Journal / source
Axioms
Volume
15
Issue
1
Pages
73–73
Publication date
20 January 2026
Language
EN