Abstract:
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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