A criterion for asymptotic stability of a system of two differential equations with homogeneous right-hand sides. (Russian) Zbl 0631.34063

Uteshev, A. Yu.; Shulyak, S. G.

Differ. Uravn. 23, No. 6, 1009-1014 (1987).

The authors consider the system of differential equations \(\dot x=P(x,y)\), \(\dot y=Q(x,y)\) with third order homogeneous polynomials P, Q. Necessary and sufficient conditions for the asymptotic stability of the zero solution are given in terms of radicals.

Reviewer: L.Hatvani

MSC:

34D20	Stability of solutions to ordinary differential equations
34D05	Asymptotic properties of solutions to ordinary differential equations

Keywords:

first order differential equation; asymptotic stability; radicals