The unique periodic solution of Abel's differential equation
type: Item
instance of: scholarly article
title: The unique periodic solution of Abel's differential equation
zbMATH Open document ID: 1456.34042
DOI: 10.1155/2020/9814829
author: Ni Hua
published in: Journal of Mathematics
publication date: 2020-07-15T00:00:00Z
review text: Consider the scalar differential equation \[ \frac{{dx}}{{dt}} = a(t) x^3 + b(t) x^2 + c(t) x+ d(t) \tag{1} \] under the assumption that \(a,b,c,d\) are continuous \(\omega\)-periodic functions. The authors prove that under the additional conditions (\(i\)). \( a(t) <0 \quad (a(t)>0)\) (\(ii\)). \(b^2(t)-3a(t)<0\) equation (1) has a unique \(\omega\)-periodic solution which is asymptotically stable (unstable).
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 7221162
zbMATH Keywords: Abel differential equation
zbMATH Keywords: periodic solution
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/9814829
OpenAlex ID: W3032778607
Wikidata QID: Q115243743
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description: scientific article; zbMATH DE number 7221162