@article{Shammakh2025, 
author = {Wafa M. Shammakh and Raghad D. Alqarni and Hadeel Z. Alzumi and Abdeljabbar Ghanmi},
title = {Multiplicityof solution for a singular problem involving the    φ-Hilfer derivative and variable exponents},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {4524-4539},
keywords = {variational methods, Nehari manifold, Sobolev space with variable exponents, φ-Hilfer derivative},
url = {https://www.sciopen.com/article/10.3934/math.2025209},
doi = {10.3934/math.2025209},
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.}
}