Upper estimates for the number of periodic solutions to multi-dimensional systems

The maximal number of zeros of multi-dimensional real analytic maps with small parameter is studied by means of the multi-dimensional generalization of Rouché's theorem. The obtained result is applied to study the maximal number of periodic solutions to multi-dimensional differential systems. A...

Full description

Saved in:
Bibliographic Details
Published in:Journal of Differential Equations 2019-06, Vol.266 (12), p.8281-8293
Main Authors: Han, Maoan, Sun, Hao, Balanov, Zalman
Format: Article
Language:English
Subjects:
Averaging method
Bifurcation function
Multiplicity
Periodic solution
Rouché's theorem
Topological index
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The maximal number of zeros of multi-dimensional real analytic maps with small parameter is studied by means of the multi-dimensional generalization of Rouché's theorem. The obtained result is applied to study the maximal number of periodic solutions to multi-dimensional differential systems. An application to a class of three-dimensional autonomous systems is given.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2018.12.034