Variational approach to fractional Sturm-Liouville equations with mixed impulses

Tingting Xue; Tingting Xue

doi:10.3934/era.2025308

Electronic Research Archive

2025, Volume 33, Issue 11: 6998-7016. doi: 10.3934/era.2025308

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Research article

Variational approach to fractional Sturm-Liouville equations with mixed impulses

Tingting Xue ^,

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

Received: 17 September 2025 Revised: 28 October 2025 Accepted: 13 November 2025 Published: 20 November 2025

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.
- Sturm-Liouville equation,
- mixed boundary conditions,
- non-instantaneous impulses,
- instantaneous impulses,
- variational methods
Citation: Tingting Xue. Variational approach to fractional Sturm-Liouville equations with mixed impulses[J]. Electronic Research Archive, 2025, 33(11): 6998-7016. doi: 10.3934/era.2025308

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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.

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