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Bubbling solutions of fourth order mean field equations on \(\mathbb{S}^{4}\)

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Abstract

In this paper, we first establish the existence of blow-up solutions with two antipodal points to the fourth order mean field equations on \(\mathbb{S}^{4}\). Moreover, we construct non-axially symmetric solutions with blow-up points at the vertices of regular configurations, i.e., equilateral triangles on a great circle, regular tetrahedrons, cubes, octahedrons, icosahedrons and dodecahedrons. The bubbling rates of these blow-up solutions rely on various bubbling configurations.

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Acknowledgements

The first author was supported by National Science Foundation of USA (Grant No. DMS-1901914). The second author was supported by National Natural Science Foundation of China (Grant Nos. 12101612 and 12171456).

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Authors and Affiliations

  1. Department of Mathematics, The University of Texas at San Antonio, San Antonio, TX, 78249, USA

    Changfeng Gui

  2. School of Mathematics and Statistics, Hunan Key Laboratory of Analytical Mathematics and Applications, Central South University, Changsha, 410083, China

    Changfeng Gui, Yeyao Hu & Weihong Xie

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  1. Changfeng Gui
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  2. Yeyao Hu
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  3. Weihong Xie
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Correspondence to Yeyao Hu.

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Gui, C., Hu, Y. & Xie, W. Bubbling solutions of fourth order mean field equations on \(\mathbb{S}^{4}\). Sci. China Math. 66, 1217–1236 (2023). https://doi.org/10.1007/s11425-022-1993-x

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  • DOI: https://doi.org/10.1007/s11425-022-1993-x

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