Existence and regularity results for critical $ (p, 2) $-Laplacian equation

Lixiong Wang; Ting Liu; Lixiong Wang; Ting Liu

doi:10.3934/math.20241458

AIMS Mathematics

2024, Volume 9, Issue 11: 30186-30213. doi: 10.3934/math.20241458

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Research article

Existence and regularity results for critical $ (p, 2) $-Laplacian equation

Lixiong Wang ^{1
,
,},
Ting Liu ²

1.
School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, Hunan, China
2.
School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, Hubei, China

Received: 07 August 2024 Revised: 11 October 2024 Accepted: 15 October 2024 Published: 24 October 2024
MSC : 35B65, 35J20, 47J30

In this paper, we study a class of $ (p, 2) $-Laplacian equation with Hartree-type nonlinearity and critical exponents. Under some general assumptions and based on variational tools, we establish the existence, regularity, and symmetry of nontrivial solutions for such a problem.
- $ (p, 2) $-Laplacian equation,
- Hartree-type nonlinearity,
- variational methods,
- regularity and symmetry,
- critical exponent
Citation: Lixiong Wang, Ting Liu. Existence and regularity results for critical $ (p, 2) $-Laplacian equation[J]. AIMS Mathematics, 2024, 9(11): 30186-30213. doi: 10.3934/math.20241458

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Abstract

In this paper, we study a class of $ (p, 2) $-Laplacian equation with Hartree-type nonlinearity and critical exponents. Under some general assumptions and based on variational tools, we establish the existence, regularity, and symmetry of nontrivial solutions for such a problem.

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