Geodesic
The transfer of the Lyapunov integral criterion to two-dimensional periodic systems of second order
Matematičeskie zametki, Tome 21 (1977) no. 6, pp. 817-828.

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Two possibilities of the transfer of the Lyapunov integral criterion [1, p. 203] (see also [2; 3, p. 177]) $\omega\int_0^\omega(\tau)\,d\tau\le4$ for the boundedness of all the solutions of the scalar equation $\ddot x+a(t)x=0$ with nonnegative $\omega$-periodic function $a(t)$ to the two-dimensional systems $\ddot x=A(t)x$ with piecewise continuous $\omega$-periodic matrix coefficients are indicated. 
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     author = {N. A. Izobov},
     title = {The transfer of the {Lyapunov} integral criterion to two-dimensional periodic systems of second order},
     journal = {Matemati\v{c}eskie zametki},
     pages = {817--828},
     publisher = {mathdoc},
     volume = {21},
     number = {6},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_6_a8/}
}
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N. A. Izobov. The transfer of the Lyapunov integral criterion to two-dimensional periodic systems of second order. Matematičeskie zametki, Tome 21 (1977) no. 6, pp. 817-828. http://geodesic.mathdoc.fr/item/MZM_1977_21_6_a8/