# Article

 Title: On asymptotic properties of a strongly nonlinear differential equation  (English) Author: Adamec, Ladislav Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 Volume: 51 Issue: 1 Year: 2001 Pages: 121-126 Summary lang: English . Category: math . Summary: 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. Keyword: ordinary differential equations Keyword: asymptotic properties MSC: 34D05 MSC: 34D99 MSC: 34E99 idZBL: Zbl 1079.34528 idMR: MR1814637 . Date available: 2009-09-24T10:40:27Z Last updated: 2012-05-31 Stable URL: http://hdl.handle.net/10338.dmlcz/127631 . Reference: [Bartusek:1992] M. Bartušek: On Oscillatory Solutions of Differential Inequalities.Czechoslovak Math. J. 42 (117) (1992), 45–51. MR 1152168 Reference: [Hartman] Ph. Hartman: Ordinary Differential Equations.John Wiley, New York-London-Sydney, 1964. Zbl 0125.32102, MR 0171038 Reference: [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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