On stability of the trivial solution of a nonautonomous quasilinear system whose characteristic equation has multiple roots

Abstract

For $t \uparrow \omega, \quad \omega \leq +\infty$, we obtain sufficient conditions for Lyapunov stability of the zero solution of a specific nonautonomous quasilinear differential system in the case where the matrix of the first-degree approximation has the Jordan form with triangular blocks. Methods to reduce certain classes of general differential systems to differential systems of special type are given.