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