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

We obtain sufficient conditions for the Lyapunov stability of the trivial solution of a nonautonomous differential system of a special form ast , + . For this system, the coefficient matrix of a differential system of the first approximation has almost Jordan form with triangular blocks. We indicate methods that enable one to reduce certain classes of differential systems of the general form to special differential systems.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 8, pp. 1072–1079, August, 1994.