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Nonoscillation of the Mathieu-type half-linear differential equation and its application to the generalized Whittaker–Hill-type equation

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Abstract

The nonoscillation of Mathieu-type half-linear differential equations was investigated. The particular equation under consideration is an extension of the Mathieu equation, which has been widely applied in mechanical and electrical engineering. The investigation led to the main finding that all nontrivial solutions of the Mathieu-type half-linear differential equations are nonoscillatory under simple parametric conditions. Proving the finding requires a simple nonoscillation theorem to compare the two equations. As another application of the findings, by using a simple nonoscillation comparison theorem, we propose that all nontrivial solutions of the half-linear Whittaker–Hill-type equation do not oscillate.

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Acknowledgements

I would like to thank Editage (www.editage.com) for English language editing. This work was supported by JSPS KAKENHI Grant-in-Aid for Early-Career Scientists [Grant Number JP22K13933].

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  1. Department of Electronic Control Engineering, National Institute of Technology (KOSEN), Hiroshima College, Toyota-gun, 725-0231, Japan

    Kazuki Ishibashi

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  1. Kazuki Ishibashi
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Correspondence to Kazuki Ishibashi.

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Communicated by Adrian Constantin.

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Ishibashi, K. Nonoscillation of the Mathieu-type half-linear differential equation and its application to the generalized Whittaker–Hill-type equation. Monatsh Math 198, 741–756 (2022). https://doi.org/10.1007/s00605-022-01720-2

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  • DOI: https://doi.org/10.1007/s00605-022-01720-2

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