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Research Article | Open Access

Variational approach to fractional Sturm-Liouville equations with mixed impulses

School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830000, China
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Abstract

This research focused on solving fractional Sturm-Liouville equations subject to mixed boundary conditions and a combination of instantaneous and non-instantaneous impulses. Through the use of variational methods, the existence of both solutions and multiple solutions for the aforementioned problem was established under assumptions that were weaker than the classical superlinear Ambrosetti-Rabinowitz type growth requirement. Finally, the examples demonstrated the validity of the paper's results.

Keywords

Sturm-Liouville equationmixed boundary conditionsnon-instantaneous impulsesinstantaneous impulsesvariational methods

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Electronic Research Archive
Volume 33 Issue 11,
November 2025
Pages 6998-7016
DOI: 10.3934/era.2025308

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Cite this article:
Xue T. Variational approach to fractional Sturm-Liouville equations with mixed impulses. Electronic Research Archive, 2025, 33(11): 6998-7016. https://doi.org/10.3934/era.2025308

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Received: 17 September 2025
Revised: 28 October 2025
Accepted: 13 November 2025
Published: 20 November 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)