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