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- Title
On Periodic Solutions of a Second-Order Ordinary Differential Equation.
- Authors
Abramov, V. V.; Liskina, E. Yu.
- Abstract
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.
- Subjects
ORDINARY differential equations; DIFFERENTIAL equations; NONLINEAR oscillators
- Publication
Journal of Mathematical Sciences, 2024, Vol 281, Issue 3, p353
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-024-07109-w