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Research Article | Open Access

Multiplicityof solution for a singular problem involving the φ-Hilfer derivative and variable exponents

Wafa M. Shammakh( ), Raghad D. Alqarni, Hadeel Z. Alzumi, Abdeljabbar Ghanmi
Department of Mathematics and Statistics, Faculty of Sciences, University of Jeddah, Jeddah, Saudi Arabia
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Abstract

This paper dealt with the existence of multiple solutions for some singular p ( s )-Laplacian problems involving the φ-Hilfer derivative. Precisely, we combined the variational method with the Nehari manifold to prove that such a problem admited two nontrivial solutions. An example was presented to illustrate the effectiveness of our main result.

Keywords

variational methodsNehari manifoldSobolev space with variable exponentsφ-Hilfer derivative
CLC number: 31B30, 35J35, 35J60

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AIMS Mathematics
Volume 10 Issue 3,
March 2025
Pages 4524-4539
DOI: 10.3934/math.2025209

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Cite this article:
Shammakh WM, Alqarni RD, Alzumi HZ, et al. Multiplicityof solution for a singular problem involving the φ-Hilfer derivative and variable exponents. AIMS Mathematics, 2025, 10(3): 4524-4539. https://doi.org/10.3934/math.2025209

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Received: 30 December 2024
Revised: 03 February 2025
Accepted: 24 February 2025
Published: 15 March 2025
©2025 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)