Min-max method for some classes of Kirchhoff problems involving the $ \psi $-Hilfer fractional derivative-Reference-Cited by-同舟云学术

Min-max method for some classes of Kirchhoff problems involving the $ \psi $-Hilfer fractional derivative

Published:2023 Issue:7 Volume:8 Page:16308-16319
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Azumi Hadeel Zaki Mohammed¹,Shammakh Wafa Mohammed Ahmed¹,Ghanmi Abdeljabbar²

Affiliation:

1. Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 21493, Saudi Arabia

2. Faculté des Sciences de Tunis, LR10ES09 Modélisation mathématique, analyse harmonique et théorie du potentiel, Université de Tunis El Manar, Tunis 2092, Tunisie

Abstract

<abstract><p>In this work, we develop some variational settings related to some singular $ p $-Kirchhoff problems involving the $ \psi $-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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference31 articles.

1. R. P. Agarwal, M. Benchohra, S. Hamani, Boundary value problems for fractional differential equations, Georgian Math. J., 16 (2009), 401–411. https://doi.org/10.1515/GMJ.2009.401

2. K. B. Ali, A. Ghanmi, K. Kefi, Existence of solutions for fractional differential equations with Dirichlet boundary conditions, Electron. J. Differ. Eq., 2016 (2016), 116.

3. R. Almeida, A Caputo fractional derivative of a function with respect to another function, Commun. Nonlinear Sci., 44 (2017), 460–481. https://doi.org/10.1016/j.cnsns.2016.09.006

4. R. Alsaedi, A. Ghanmi, Variational approach for the Kirchhoff problem involving the $p$-Laplace operator and the $\psi$-Hilfer derivative, Math. Method. Appl. Sci., 2023. https://doi.org/10.1002/mma.9053

5. J. K. Brooks, Equicontinuous sets of measures and applications to Vitali's integral convergence theorem and control measures, Adv. Math., 10 (1973), 165–171. https://doi.org/10.1016/0001-8708(73)90104-7

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