On multiple solutions for an elliptic problem involving Leray–Lions operator, Hardy potential and indefinite weight with mixed boundary conditions

Khaled Kefi; Mohammed M. Al-Shomrani; Khaled Kefi; Mohammed M. Al-Shomrani

doi:10.3934/math.2025251

AIMS Mathematics

2025, Volume 10, Issue 3: 5444-5455. doi: 10.3934/math.2025251

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Research article

On multiple solutions for an elliptic problem involving Leray–Lions operator, Hardy potential and indefinite weight with mixed boundary conditions

Khaled Kefi ^{1
,
,},
Mohammed M. Al-Shomrani ^{2
,
,}

1.
Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 20 January 2025 Revised: 03 March 2025 Accepted: 05 March 2025 Published: 11 March 2025
MSC : 35J15, 35J20, 35J25

This paper concentrates on establishing the existence of multiple weak solutions for a specific type of elliptic equations that involve a Hardy potential and have mixed boundary conditions. The main goal of the study is to establish an existence result of at least three different weak solutions thanks to variational techniques, Hardy inequality, and a particular theorem called the Bonanno–Marano type three critical points theorem.
- two parameters,
- elliptic equations,
- mixed boundary conditions,
- $ p(x) $-Laplacian,
- Hardy term
Citation: Khaled Kefi, Mohammed M. Al-Shomrani. On multiple solutions for an elliptic problem involving Leray–Lions operator, Hardy potential and indefinite weight with mixed boundary conditions[J]. AIMS Mathematics, 2025, 10(3): 5444-5455. doi: 10.3934/math.2025251

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Abstract

This paper concentrates on establishing the existence of multiple weak solutions for a specific type of elliptic equations that involve a Hardy potential and have mixed boundary conditions. The main goal of the study is to establish an existence result of at least three different weak solutions thanks to variational techniques, Hardy inequality, and a particular theorem called the Bonanno–Marano type three critical points theorem.

References

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