Stability of characteristic vectors of a class of linear systems of differential equations (Q2479649)

The author introduces the characteristic vectors of solutions to a real linear system \[ \frac {dx}{dt}=A(t)x \] and a perturbed system \[ \frac {dz}{dt}=(A(t)+Q(t))z, \] where \(x\in \mathbb{R}^n,\;A(t)\) is a piecewise continuous and bounded on \([t_0,+\infty)\) matrix and \(Q(t)\) is a piecewise continuous matrix for \(t\geq t_0\) such that \(\| Q(t)\|< \gamma(\prod_{i=0}^{m-1}\ln_i(t))^{-1}\) with an iterated logarithm \(\ln_i(t),\;i=1,dots,\;m-1.\) The main result declares that a considered system regular of the order \(m\) has an n-fold characteristic vector which is stable of the order \(m\).