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

Author

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  • 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, Hindawi, vol. 2014, pages 1-14, July.
    • Handle: RePEc:hin:jnlaaa:258159
    DOI: 10.1155/2014/258159
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    Cited by:

    1. Hasil, Petr & Veselý, Michal, 2019. "Modified Prüfer angle and conditional oscillation of perturbed linear and half-linear differential equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 788-809.
    2. Yamanaka, Yusuke & Yamaoka, Naoto, 2021. "Oscillation and nonoscillation theorems for Meissner’s equation," Applied Mathematics and Computation, Elsevier, vol. 388(C).

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