# Article

 Title: On a conjecture about an integral criterion for oscillation  (English) Author: Elias, Uri Author: Škerlík, Anton Language: English Journal: Archivum Mathematicum ISSN: 0044-8753 (print) ISSN: 1212-5059 (online) Volume: 34 Issue: 3 Year: 1998 Pages: 393-399 Summary lang: English . Category: math . Summary: We discuss an open question of Kiguradze and Chanturia about Property $A$ and Property $B$ for the equation $y^{(n)} + py = 0$. The proposed integral criterion is proved in a few cases. Keyword: oscillation Keyword: Property A Keyword: Property B MSC: 34C10 idZBL: Zbl 0973.34022 idMR: MR1662060 . Date available: 2009-02-17T10:14:43Z Last updated: 2012-05-10 Stable URL: http://hdl.handle.net/10338.dmlcz/107666 . Reference: [K] Kiguradze, I. T. and Chanturia, T. A.: Asymptotic properties of solutions of nonautonomous ordinary differential equations.Kluwer Publishers, Dordrecht, 1993. MR 1220223 Reference: [E] Elias, U.: Oscillation theory of two-term differential equations.Kluwer Publishers, Dordrecht, 1997. Zbl 0878.34022, MR 1445292 Reference: [S1] Škerlík, A.: An integral condition of oscillation for the equation $y^{\prime \prime \prime } + p(t)y^{\prime } + q(t)y = 0$ with nonnegative coefficients.Arch. Math. (Brno) 31 (1995), 151-161. MR 1357983 Reference: [S2] Škerlík, A.: An integral condition of Property $A$ and $B$ for linear differential equation of third order.Proceedings of the Conference on Ordinary Differential Equations Poprad, Slovac Republic (1994), 81-85. .

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