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Oscillation and nonoscillation theorems for Meissner’s equation

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  • Yamanaka, Yusuke
  • Yamaoka, Naoto

Abstract

The purpose of this paper is to present a pair of an oscillation theorem and a nonoscillation theorem for Meissner’s equation which is the special case of Hill’s equation. Proof is given by means of the Riccati technique. Furthermore, using Liouville transformation and Sturm’s comparison theorem, we show a relation between Meissner equations and Cauchy-Euler equations. Moreover, by numerical computations, we give an approximate value which is the borderline between oscillation and nonoscillation for Meissner equations.

Suggested Citation

  • Yamanaka, Yusuke & Yamaoka, Naoto, 2021. "Oscillation and nonoscillation theorems for Meissner’s equation," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    • Handle: RePEc:eee:apmaco:v:388:y:2021:i:c:s0096300320304847
    DOI: 10.1016/j.amc.2020.125526
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    References listed on IDEAS

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    1. Sugie, Jitsuro & Ishibashi, Kazuki, 2019. "Nonoscillation of Mathieu equations with two frequencies," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 491-499.
    2. 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.
    3. 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.
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    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.

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