Geodesic
Boundedness and stability criteria for linear ordinary differential equations of the second order
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2013), pp. 11-18

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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. 
@article{IVM_2013_12_a1,
     author = {G. A. Grigoryan},
     title = {Boundedness and stability criteria for linear ordinary differential equations of the second order},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {11--18},
     publisher = {mathdoc},
     number = {12},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_12_a1/}
}
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G. A. Grigoryan. Boundedness and stability criteria for linear ordinary differential equations of the second order. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2013), pp. 11-18. http://geodesic.mathdoc.fr/item/IVM_2013_12_a1/