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Global monotonicity and oscillation for second order differential equation

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Abstract

Oscillatory properties of the second order nonlinear equation

$$\left( {r\left( t \right)x'} \right)^\prime + q\left( t \right)f\left( x \right) = 0$$

are investigated. In particular, criteria for the existence of at least one oscillatory solution and for the global monotonicity properties of nonoscillatory solutions are established. The possible coexistence of oscillatory and nonoscillatory solutions is studied too.

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Authors and Affiliations

  1. Department of Mathematics, Masaryk University, Janáčkovo nám. 2a, 662 95, Brno, Czech Republic

    M. Bartušek

  2. Department of Electronics and Telecomunications, University of Florence, Via S. Marta 3, 501 39, Firenze, Italy

    M. Cecchi

  3. Department of Mathematics, Masaryk University, Janáčkovo nám. 2a, 662 95, Brno, Czech Republic

    Z. Došlá

  4. Department of Electronics and Telecomunications, University of Florence, Via S. Marta 3, 501 39, Firenze, Italy

    M. Marini

Authors
  1. M. Bartušek
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  2. M. Cecchi
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  3. Z. Došlá
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  4. M. Marini
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Bartušek, M., Cecchi, M., Došlá, Z. et al. Global monotonicity and oscillation for second order differential equation. Czech Math J 55, 209–222 (2005). https://doi.org/10.1007/s10587-005-0016-y

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  • DOI: https://doi.org/10.1007/s10587-005-0016-y

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