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Research Article | Open Access

On Kirchhoff type problems with singular nonlinearity in closed manifolds

Nanbo Chen1,2, Honghong Liang1, Xiaochun Liu3( )
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
Center for Applied Mathematics of Guangxi (GUET), Guilin, 541002, China
School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China
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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≥3. Existence and uniqueness of a positive weak solution were obtained under certain assumptions with the help of the variation methods and some analysis techniques.

Keywords

Kirchhoff equationssingularitycritical exponentclosed manifoldsvariational methods
CLC number: 35J20, 58J05

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 21397-21413
DOI: 10.3934/math.20241039

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Cite this article:
Chen N, Liang H, Liu X. On Kirchhoff type problems with singular nonlinearity in closed manifolds. AIMS Mathematics, 2024, 9(8): 21397-21413. https://doi.org/10.3934/math.20241039

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Received: 11 February 2024
Revised: 01 June 2024
Accepted: 19 June 2024
Published: 15 August 2024
©2024 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)