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; Deke Wu; Hongmin Suo; Linyan Peng; Guaiqi Tian; Changmu Chu

doi:10.3934/math.2022443

AIMS Mathematics

2022, Volume 7, Issue 5: 7909-7935. doi: 10.3934/math.2022443

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

College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, China

Received: 12 November 2021 Revised: 25 January 2022 Accepted: 05 February 2022 Published: 22 February 2022
MSC : 35B33, 35J75

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) $.
- multiple positive solutions,
- critical exponents,
- singularity,
- Nehari method,
- variational method
Citation: Deke Wu, Hongmin Suo, Linyan Peng, Guaiqi Tian, Changmu Chu. Existence and multiplicity of positive solutions for a class of Kirchhoff type problems with singularity and critical exponents[J]. AIMS Mathematics, 2022, 7(5): 7909-7935. doi: 10.3934/math.2022443

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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) $.

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