Аналог теореми Єругiна для систем диференцiальних рiвнянь другого порядку

Abstract

The theorem about equivalence in Lyapunov’s sense of two systems of differential equations of the second order which is an analog of the well-known theorem of M. P. Erugin about the equivalence of systems of differential equations of the first order is proved. Using this theorem, several statements about structural transformations of systems of differential equations of the second order which facilitate the research of stability of the trivial solution are obtained.