Reducibility of nonlinear differential equations to block-triangular form. (English. Russian original) Zbl 1031.34038

Pashutkin, D. V.

Russ. Math. 45, No. 6, 47-54 (2001); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2001, No. 6, 50-57 (2001).

The reducibility of nonlinear differential equations \[ \dot{x}=f(t,x), x \in\mathbb{R}^n, t \in\mathbb{R},\tag{1} \] in a group \(LG\) of Lyapunov’s transformations is investigated. A sufficient condition for the reducibility of equation (1) to a block-triangular differential equation and a necessary and sufficient condition for the reducibility to a diagonal differential equation are obtained.

Reviewer: Natalia Medvedeva (Chelyabinsk)

MSC:

34C20

Transformation and reduction of ordinary differential equations and systems, normal forms

Keywords:

nonlinear differential equations; reducibility; block-triangular differential equation