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Research Article | Open Access

Min-max method for some classes of Kirchhoff problems involving the ψ-Hilfer fractional derivative

Hadeel Zaki Mohammed Azumi1( ), Wafa Mohammed Ahmed Shammakh1, Abdeljabbar Ghanmi2
Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 21493, Saudi Arabia
Faculté des Sciences de Tunis, LR10ES09 Modélisation mathématique, analyse harmonique et théorie du potentiel, Université de Tunis El Manar, Tunis 2092, Tunisie
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Abstract

In this work, we develop some variational settings related to some singular p-Kirchhoff problems involving the ψ-Hilfer fractional derivative. More precisely, we combine the variational method with the min-max method in order to prove the existence of nontrivial solutions for the given problem. Our main result generalizes previous ones in the literature.

Keywords

variational methodsmin-max methodp-Laplacian operatorψ-Hilfer operators
CLC number: 31B30, 35J35, 35J60

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 16308-16319
DOI: 10.3934/math.2023835

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Cite this article:
Azumi HZM, Shammakh WMA, Ghanmi A. Min-max method for some classes of Kirchhoff problems involving the ψ-Hilfer fractional derivative. AIMS Mathematics, 2023, 8(7): 16308-16319. https://doi.org/10.3934/math.2023835

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Received: 09 March 2023
Revised: 19 April 2023
Accepted: 23 April 2023
Published: 15 July 2023
©2023 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)