On Kirchhoff type problems with singular nonlinearity in closed manifolds

Nanbo Chen; Honghong Liang; Xiaochun Liu; Nanbo Chen; Honghong Liang; Xiaochun Liu

doi:10.3934/math.20241039

AIMS Mathematics

2024, Volume 9, Issue 8: 21397-21413. doi: 10.3934/math.20241039

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Research article

On Kirchhoff type problems with singular nonlinearity in closed manifolds

1.
School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, 541002, China
2.
Center for Applied Mathematics of Guangxi (GUET), Guilin, 541002, China
3.
School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

Received: 11 February 2024 Revised: 01 June 2024 Accepted: 19 June 2024 Published: 03 July 2024
MSC : 35J20, 58J05

This paper dealt with a class of Kirchhoff type equations involving singular nonlinearity in a closed Riemannian manifold $ (M, g) $ of dimension $ n\ge3 $. Existence and uniqueness of a positive weak solution were obtained under certain assumptions with the help of the variation methods and some analysis techniques.
- Kirchhoff equations,
- singularity,
- critical exponent,
- closed manifolds,
- variational methods
Citation: Nanbo Chen, Honghong Liang, Xiaochun Liu. On Kirchhoff type problems with singular nonlinearity in closed manifolds[J]. AIMS Mathematics, 2024, 9(8): 21397-21413. doi: 10.3934/math.20241039

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Abstract

This paper dealt with a class of Kirchhoff type equations involving singular nonlinearity in a closed Riemannian manifold $ (M, g) $ of dimension $ n\ge3 $. Existence and uniqueness of a positive weak solution were obtained under certain assumptions with the help of the variation methods and some analysis techniques.

References

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