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Research Article | Open Access

Infinitely many solutions for a critical p(x)-Kirchhoff equation with Steklov boundary value

Khaled Kefi1( ), Abdeljabbar Ghanmi2, Abdelhakim Sahbani3, Mohammed M. Al-Shomrani4
Faculty of Computing and Information Technology, Northern border University, Arar, Kingdom of Saudi Arabia
ENIT-LAMSIN, BP. 37, 1002 Tunis-Belvédère, Tunis El Manar university, Tunis, Tunisia
Faculté des Sciences de Tunis, Université de Tunis El Manar, Tunis 2092, Tunisia
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Kingdom of Saudi Arabia
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Abstract

In this paper, we aim to tackle the questions of existence and multiplicity of solutions of the p(x)-Kirchhoff problem involving critical exponent and the Steklov boundary value. Further, we research the results from the theory of variable exponent Sobolev spaces, the concentration-compactness principle, and the symmetric mountain pass theorem.

Keywords

variational methodscritical exponentthe concentration-compactness principleKirchhoff equationSteklov problem
CLC number: 35J20, 35J15, 35J25

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AIMS Mathematics
Volume 9 Issue 10,
October 2024
Pages 28361-28378
DOI: 10.3934/math.20241376

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Kefi K, Ghanmi A, Sahbani A, et al. Infinitely many solutions for a critical p(x)-Kirchhoff equation with Steklov boundary value. AIMS Mathematics, 2024, 9(10): 28361-28378. https://doi.org/10.3934/math.20241376

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Received: 11 July 2024
Revised: 17 August 2024
Accepted: 04 September 2024
Published: 15 October 2024
©2024 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)