On Periodic Solutions of a Second-Order Ordinary Differential Equation

We consider a differential equation containing first- and second-order forms with respect to the phase variable and its derivative with constant coefficients and a periodic inhomogeneity. Using the method of constructing a positively invariant rectangular domain, we examine the existence of a asympt...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 281; no. 3; pp. 353 - 358
Main Authors Abramov, V. V., Liskina, E. Yu
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 10.05.2024
Springer
Springer Nature B.V
Subjects
Differential equations
Inhomogeneity
Mathematics
Mathematics and Statistics
periodic solution
34C05
qualitative theory
34C25
nonlinear oscillator
34D20
second-order differential equation
stability
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Summary:We consider a differential equation containing first- and second-order forms with respect to the phase variable and its derivative with constant coefficients and a periodic inhomogeneity. Using the method of constructing a positively invariant rectangular domain, we examine the existence of a asymptotically stable (in the Lyapunov sense) periodic solution. Criteria for the existence of a periodic solution are formulated in terms of properties of isoclines. We consider cases where the zero isocline is a nondegenerate second-order curve.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07109-w