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Oscillation of third order differential equation with damping term

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Abstract

We study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term

$$x'''(t) + q(t)x'(t) + r(t)\left| x \right|^\lambda (t)\operatorname{sgn} x(t) = 0,{\text{ }}t \geqslant 0.$$

We give conditions under which every solution of the equation above is either oscillatory or tends to zero. In case λ ⩽ 1 and if the corresponding second order differential equation h″ + q(t)h = 0 is oscillatory, we also study Kneser solutions vanishing at infinity and the existence of oscillatory solutions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Masaryk University, Kotlářská 267/2, 611 37, Brno, Czech Republic

    Miroslav Bartušek & Zuzana Došlá

Authors
  1. Miroslav Bartušek
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  2. Zuzana Došlá
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Corresponding author

Correspondence to Miroslav Bartušek.

Additional information

Dedicated to the memory of Professor Marko Švec

Research is supported by the grant GAP 201/11/0768 of the Czech Grant Agency.

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Bartušek, M., Došlá, Z. Oscillation of third order differential equation with damping term. Czech Math J 65, 301–316 (2015). https://doi.org/10.1007/s10587-015-0176-3

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  • DOI: https://doi.org/10.1007/s10587-015-0176-3

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