This article is cited 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.

UDC: 517.923

Received: 30.07.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:12, 8–15

Bibliographic databases:

•