Definition and some properties of Perron stability (Q2319420)

In this paper, the author considers the following system of ordinary differential equations \[ \dot x=f(t,x),\quad f(t,0)\equiv 0,\quad t\in[0,\infty),\quad x\in G\subset \mathbb{R}^n. \] The definitions for Perron stability, Perron asymptotic stability, Perron instability, and complete Perron instability of its zero solution are given. Perron stability and Lyapunov stability are compared. Some special cases are considered.