Triple solutions for a Leray-Lions $ p(x) $-biharmonic operator involving Hardy potential and indefinite weight

K. Kefi; Jian Liu; K. Kefi; Jian Liu

doi:10.3934/math.20241106

AIMS Mathematics

2024, Volume 9, Issue 8: 22697-22711. doi: 10.3934/math.20241106

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Research article

Triple solutions for a Leray-Lions $ p(x) $-biharmonic operator involving Hardy potential and indefinite weight

K. Kefi ^{1
,
,},
Jian Liu ²

1.
Faculty of Computing and Information Technology, Northern Border University, Rafha, Saudi Arabia
2.
School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China

Received: 14 April 2024 Revised: 10 July 2024 Accepted: 18 July 2024 Published: 23 July 2024
MSC : 35J20, 35J35, 35J60, 35G30, 46E35

Existence and multiplicity of three weak solutions for a Leray-Lions $ p(x) $-biharmonic problem involving Hardy potential and indefinite weight were proved. Our main tools combined variational methods and some critical theorems.
- critical theorem,
- Leray-Lions operator,
- Hardy potential,
- variable exponent
Citation: K. Kefi, Jian Liu. Triple solutions for a Leray-Lions $ p(x) $-biharmonic operator involving Hardy potential and indefinite weight[J]. AIMS Mathematics, 2024, 9(8): 22697-22711. doi: 10.3934/math.20241106

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Abstract

Existence and multiplicity of three weak solutions for a Leray-Lions $ p(x) $-biharmonic problem involving Hardy potential and indefinite weight were proved. Our main tools combined variational methods and some critical theorems.

References

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