Multiplicityof solution for a singular problem involving the $ \varphi $-Hilfer derivative and variable exponents

Multiplicityof solution for a singular problem involving the $ \varphi $-Hilfer derivative and variable exponents

This paper dealt with the existence of multiple solutions for some singular $ p(s) $-Laplacian problems involving the $ \varphi $-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 pr...

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Bibliographic Details
Main Authors: Wafa M. Shammakh, Raghad D. Alqarni, Hadeel Z. Alzumi, Abdeljabbar Ghanmi
Format: Article
Language:English
Published: AIMS Press 2025-03-01
Series:AIMS Mathematics
Subjects:
variational methods
nehari manifold
sobolev space with variable exponents
$ \varphi $-hilfer derivative
Online Access:https://www.aimspress.com/article/doi/10.3934/math.2025209
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Summary:This paper dealt with the existence of multiple solutions for some singular $ p(s) $-Laplacian problems involving the $ \varphi $-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.
ISSN:2473-6988

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