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 in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024-05, Vol.281 (3), p.353-358
Main Authors: Abramov, V. V., Liskina, E. Yu
Format: Article
Language:English
Subjects:
Differential equations
Inhomogeneity
Mathematics
Mathematics and Statistics
Online Access:Get full text
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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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07109-w