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

Khaled Kefi; Abdeljabbar Ghanmi; Abdelhakim Sahbani; Mohammed M. Al-Shomrani; Khaled Kefi; Abdeljabbar Ghanmi; Abdelhakim Sahbani; Mohammed M. Al-Shomrani

doi:10.3934/math.20241376

AIMS Mathematics

2024, Volume 9, Issue 10: 28361-28378. doi: 10.3934/math.20241376

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Research article

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

1.
Faculty of Computing and Information Technology, Northern border University, Arar, Kingdom of Saudi Arabia
2.
ENIT-LAMSIN, BP. 37, 1002 Tunis-Belvédère, Tunis El Manar university, Tunis, Tunisia
3.
Faculté des Sciences de Tunis, Université de Tunis El Manar, Tunis 2092, Tunisia
4.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Kingdom of Saudi Arabia

Received: 11 July 2024 Revised: 17 August 2024 Accepted: 04 September 2024 Published: 30 September 2024
MSC : 35J20, 35J15, 35J25

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.
- variational methods,
- critical exponent,
- the concentration-compactness principle,
- Kirchhoff equation,
- Steklov problem
Citation: Khaled Kefi, Abdeljabbar Ghanmi, Abdelhakim Sahbani, Mohammed M. Al-Shomrani. Infinitely many solutions for a critical $ p(x) $-Kirchhoff equation with Steklov boundary value[J]. AIMS Mathematics, 2024, 9(10): 28361-28378. doi: 10.3934/math.20241376

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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.

References

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