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Conditional Oscillation of Half‐Linear Differential Equations with Coefficients Having Mean Values

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Listed:
  • Petr Hasil
  • Robert Mařík
  • Michal Veselý

Abstract

We prove that the existence of the mean values of coefficients is sufficient for second‐order half‐linear Euler‐type differential equations to be conditionally oscillatory. We explicitly find an oscillation constant even for the considered equations whose coefficients can change sign. Our results cover known results concerning periodic and almost periodic positive coefficients and extend them to larger classes of equations. We give examples and corollaries which illustrate cases that our results solve. We also mention an application of the presented results in the theory of partial differential equations.

Suggested Citation

  • Petr Hasil & Robert Mařík & Michal Veselý, 2014. "Conditional Oscillation of Half‐Linear Differential Equations with Coefficients Having Mean Values," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:258159
    DOI: 10.1155/2014/258159
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    References listed on IDEAS

    as
    1. Ravi P. Agarwal & Said R. Grace & Donal O’Regan, 2002. "Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations," Springer Books, Springer, number 978-94-017-2515-6, March.
    2. Petr Hasil & Michal Veselý, 2012. "Critical Oscillation Constant for Difference Equations with Almost Periodic Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Petr Hasil & Michal Veselý, 2012. "Critical Oscillation Constant for Difference Equations with Almost Periodic Coefficients," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-19, October.
    4. Ondřej Došlý & Hana Funková, 2012. "Perturbations of Half‐Linear Euler Differential Equation and Transformations of Modified Riccati Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    Full references (including those not matched with items on IDEAS)

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