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ordinary differential equations; asymptotic properties
The paper describes asymptotic properties of a strongly nonlinear system $\dot{x}=f(t,x)$, $(t,x)\in \mathbb{R}\times \mathbb{R}^n$. The existence of an $\lfloor {}n/2\rfloor $ parametric family of solutions tending to zero is proved. Conditions posed on the system try to be independent of its linear approximation.
[Bartusek:1992] M. Bartušek: On Oscillatory Solutions of Differential Inequalities. Czechoslovak Math. J. 42 (117) (1992), 45–51. MR 1152168
[Hartman] Ph. Hartman: Ordinary Differential Equations. John Wiley, New York-London-Sydney, 1964. MR 0171038 | Zbl 0125.32102
[Kiguradze-Chanturia:1990] I. T. Kiguradze and T. A. Chanturiya: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations. Moskva, Nauka, 1990. (Russian)
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