Globalna Asymptotyczna Stateczność Pewnego Układu Nieliniowego

In the paper the following set of equations is considered (1), which represents a certain class of nonlinear system of proper vibrations. On the basis of the theorem of overall asymptotic stability of the zero solution of the P. Hartman-Cz. Olech’s set of differential equations, the following theorem has been proved.
Let a>-0, b>0, c>0, and let ϕ(0)=0, ϕ ϵ C1. If φ'(u)≥b/c^2-a/b, when b^2≥2ac^2 and φ'(u)≥a/b, when b^2<2ac^2 for every solution u, then the zero solution of the set (1) is overall asymptotically stable.