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Research Article | Open Access

Multiple solutions for discontinuous fractional p-Laplacian problems

Department of Applied Mathematics, Huaihua University, Huaihua 418000, China
Department of Mathematics, Shaoyang University, Shaoyang, Hunan 422000, China
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Abstract

In this paper, We studied a class of fractional p-Laplacian equations with nonsmooth potential. By nonsmooth analysis, nonsmooth critical point theory, and truncation techniques, we established two multiplicity theorems: One guaranteeing the existence of at least four solutions, and the other ensuring the existence of at least two solutions. In our approach, we addressed the challenges posed by the nonsmoothness of the potential, and the results extended the nonlocal problems with discontinuous nonlinearities.

Keywords

fractional p-Laplaciannonsmooth critical pointlocally Lipschitzmultiple solutions
CLC number: 34A36, 35K57, 49J52

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AIMS Mathematics
Volume 11 Issue 5,
May 2026
Pages 13500-13529
DOI: 10.3934/math.2026556

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Yuan Z. Multiple solutions for discontinuous fractional p-Laplacian problems. AIMS Mathematics, 2026, 11(5): 13500-13529. https://doi.org/10.3934/math.2026556

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Received: 27 November 2025
Revised: 15 April 2026
Accepted: 29 April 2026
Published: 15 May 2026
©2026 the Author(s), licensee AIMS Press.

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