On the question of existence of a Lyapunov polynomial function. (Russian) Zbl 0698.34045

Uteshev, A. Yu.

Differ. Uravn. 25, No. 11, 2010-2013 (1989).

The following theorem is proved: for every positive integer m there exist homogeneous polynomials P(x,y), Q(x,y) of the third degree such that the derivative with respect to the system \(\dot x=P(x,y)\), \(\dot y=Q(x,y)\) of any arbitrary homogeneous polynomial of degree m is not negative definite.

Reviewer: L.Hatvani

MSC:

34D20

Stability of solutions to ordinary differential equations

Keywords:

homogeneous polynomial