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Modified Prüfer angle and conditional oscillation of perturbed linear and half-linear differential equations

Author

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  • Hasil, Petr
  • Veselý, Michal

Abstract

The research and results described in this paper belong to the qualitative theory of differential equations (more precisely, the partial differential equations with the one-dimensional p-Laplacian). Using a method whose core is formed by the Prüfer technique, we identify a borderline case between oscillatory and non-oscillatory equations. Moreover, we are able to decide whether the studied equations are oscillatory or not even in the so-called critical (i.e., the borderline) case. The advantage of our approach is the fact that we obtain new and strong results for linear and half-linear equations (i.e., the equations with the one-dimensional p-Laplacian) at the same time. In addition, we are able to work with equations whose coefficients are non-constant and non-periodic. The novelty of our results is documented by examples and corollaries.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:788-809
    DOI: 10.1016/j.amc.2019.06.027
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    References listed on IDEAS

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    1. Hasil, Petr & Veselý, Michal, 2015. "Limit periodic homogeneous linear difference systems," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 958-972.
    2. 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.
    3. Adil Misir & Banu Mermerkaya, 2017. "Critical Oscillation Constant for Euler Type Half-Linear Differential Equation Having Multi-Different Periodic Coefficients," International Journal of Differential Equations, Hindawi, vol. 2017, pages 1-8, February.
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    Citations

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    Cited by:

    1. 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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    2. Petr Hasil & Michal Veselý, 2023. "Oscillation and nonoscillation of perturbed nonlinear equations with p‐Laplacian," Mathematische Nachrichten, Wiley Blackwell, vol. 296(7), pages 2809-2837, July.

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