Averaging principle on semi‐axis for semi‐linear differential equations

We establish an averaging principle on the real semi‐axis for semi‐linear equation with unbounded closed linear operator and asymptotically Poisson stable (in particular, asymptotically stationary, asymptotically periodic, asymptotically quasi‐periodic, asymptotically almost periodic, asymptotically...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische Nachrichten 2024-11
Main Author: Cheban, David
Format: Article
Language:English
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We establish an averaging principle on the real semi‐axis for semi‐linear equation with unbounded closed linear operator and asymptotically Poisson stable (in particular, asymptotically stationary, asymptotically periodic, asymptotically quasi‐periodic, asymptotically almost periodic, asymptotically almost automorphic, asymptotically recurrent) coefficients. Under some conditions, we prove that there exists at least one solution, which possesses the same asymptotically recurrence property as the coefficients, in a small neighborhood of the stationary solution to the averaged equation, and this solution converges to the stationary solution of averaged equation uniformly on the real semi‐axis when the small parameter approaches to zero.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202300392