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Research Article | Open Access

Existence and multiplicity results for a singular fourth-order elliptic system involving critical homogeneous nonlinearities

Zhiying Deng1( ), Yisheng Huang2
School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
Department of Mathematics, Soochow University, Suzhou 215006, Jiangsu, China
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Abstract

This paper deals with a singular fourth-order elliptic system involving critical homogeneous nonlinearities. The existence and multiplicity results of group invariant solutions are established by variational methods and the Hardy-Rellich inequality.

Keywords

Hardy-Rellich inequalitygroup invariant solutionvariational methodsfourth-order elliptic system
CLC number: 35J35, 35J40, 35J50

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AIMS Mathematics
Volume 8 Issue 4,
April 2023
Pages 9054-9073
DOI: 10.3934/math.2023453

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Cite this article:
Deng Z, Huang Y. Existence and multiplicity results for a singular fourth-order elliptic system involving critical homogeneous nonlinearities. AIMS Mathematics, 2023, 8(4): 9054-9073. https://doi.org/10.3934/math.2023453

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Received: 28 October 2022
Revised: 02 February 2023
Accepted: 05 February 2023
Published: 15 April 2023
©2023 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)