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Research Article | Open Access

Existence and multiplicity of positive solutions for a class of Kirchhoff type problems with singularity and critical exponents

Deke Wu, Hongmin Suo( ), Linyan Peng, Guaiqi Tian, Changmu Chu
College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, China
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Abstract

In this paper, we study the multiplicity results of positive solutions for a class of Kirchhoff type problems with singularity and critical exponents. Combining with the Nehari method and variational method, we prove the existence of positive ground state solutions. Furthermore, we obtain a relationship between the number of positive solutions and the topology of the global maximum set of Q ( x ).

Keywords

multiple positive solutionscritical exponentssingularityNehari methodvariational method
CLC number: 35B33, 35J75

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 7909-7935
DOI: 10.3934/math.2022443

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Cite this article:
Wu D, Suo H, Peng L, et al. Existence and multiplicity of positive solutions for a class of Kirchhoff type problems with singularity and critical exponents. AIMS Mathematics, 2022, 7(5): 7909-7935. https://doi.org/10.3934/math.2022443

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Received: 12 November 2021
Revised: 25 January 2022
Accepted: 05 February 2022
Published: 15 May 2022
©2022 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)