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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 12, Pages 11–18
(Mi ivm8850)
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This article is cited in 7 scientific papers (total in 7 papers)
Boundedness and stability criteria for linear ordinary differential equations of the second order
G. A. Grigoryan Institute of Mathematics of NAS of Armenia, 24/5 Marshal Bagramyan str., Erevan, 0019 Republic of Armeniya
Abstract:
We establish some correlations for solutions of ordinary differential equations and the imaginary part of the complex solution of the corresponding Riccati equation. On the basis of these correlations and the I. M. Sobol' theorem we prove some new stability and boundedness criteria for linear equations of the second order.
Keywords:
complex solution of Riccati equation, I.M. Sobol' theorem, boundedness, Lyapunov stability, asymptotic stability.
Received: 30.07.2012
Citation:
G. A. Grigoryan, “Boundedness and stability criteria for linear ordinary differential equations of the second order”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 12, 11–18; Russian Math. (Iz. VUZ), 57:12 (2013), 8–15
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https://www.mathnet.ru/eng/ivm8850 https://www.mathnet.ru/eng/ivm/y2013/i12/p11
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Abstract page: | 466 | Full-text PDF : | 138 | References: | 63 | First page: | 12 |
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