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Research Article | Open Access

Existence and multiplicity of solutions for critical Choquard-Kirchhoff type equations with variable growth

Lulu Tao1, Rui He1, Sihua Liang1, Rui Niu2( )
College of Mathematics, Changchun Normal University, Changchun 130032, China
College of Science, Heilongjiang Institute of Technology, Harbin 150050, China
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Abstract

We prove the existence and multiplicity of solutions for a class of Choquard-Kirchhoff type equations with variable exponents and critical reaction. Because the appearance of the critical reaction, we deal with the lack of compactness by using the concentration-compactness principle. In particular, we discuss the main results in non-degenerate and degenerate cases. And we apply combination of Krasnoselskii genus and the Hardy-Littlewood-Sobolev inequality to get the results of existence and multiplicity.

Keywords

Choquard equationcritical nonlinearityconcentration-compactness principlesvariational methods
CLC number: 35J20, 35J60, 35J62

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AIMS Mathematics
Volume 8 Issue 2,
February 2023
Pages 3026-3048
DOI: 10.3934/math.2023156

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Cite this article:
Tao L, He R, Liang S, et al. Existence and multiplicity of solutions for critical Choquard-Kirchhoff type equations with variable growth. AIMS Mathematics, 2023, 8(2): 3026-3048. https://doi.org/10.3934/math.2023156

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Received: 15 September 2022
Revised: 26 October 2022
Accepted: 04 November 2022
Published: 15 February 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)