On the uniformness of estimates for the norms of solutions of exponentially dichotomous systems (Q610332)

The author considers the linear differential equation \[ {dx\over dt}= A(t)x,\quad x\in\mathbb{R}^n,\quad t\geq 0.\tag{1} \] By \(Z_A(\cdot)\) is denote the linear subspace of the maximum dimension in \(X_A\) that consists of solutions tending to zero as \(t\to\infty\). \(X_A\) consists of solutions tending to a zero as \(t\to\infty\). By help of \(Z_A(\cdot)\) the existence of one nonexponentially dichotomous system (1) is proved.