Critical fractional Kirchhoff problems: Uniqueness and Nondegeneracy
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915612404482048 |
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| author | Yang, Zhipeng Yu, Yuanyang |
| author_facet | Yang, Zhipeng Yu, Yuanyang |
| contents | In this paper, we consider the following critical fractional Kirchhoff equation \begin{equation*} \Big(a+b{\int_{\mathbb{R}^{N}}}|(-Δ)^{\frac{s}{2}}u|^2dx\Big)(-Δ)^su=|u|^{2^*_s-2}u,\quad \text{in}\ \mathbb{R}^{N}, \end{equation*} where $a,b>0$, $\frac{N}{4}<s<1$, $2^*_s=\frac{2N}{N-2s}$ and $(-Δ)^s$ is the fractional Laplacian. We prove the uniqueness and nondegeneracy of positive solutions to the problem, which can be used to study the singular perturbation problems concerning fractional Kirchhoff equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_20277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Critical fractional Kirchhoff problems: Uniqueness and Nondegeneracy Yang, Zhipeng Yu, Yuanyang Analysis of PDEs 35R11, 35A15, 47G20 In this paper, we consider the following critical fractional Kirchhoff equation \begin{equation*} \Big(a+b{\int_{\mathbb{R}^{N}}}|(-Δ)^{\frac{s}{2}}u|^2dx\Big)(-Δ)^su=|u|^{2^*_s-2}u,\quad \text{in}\ \mathbb{R}^{N}, \end{equation*} where $a,b>0$, $\frac{N}{4}<s<1$, $2^*_s=\frac{2N}{N-2s}$ and $(-Δ)^s$ is the fractional Laplacian. We prove the uniqueness and nondegeneracy of positive solutions to the problem, which can be used to study the singular perturbation problems concerning fractional Kirchhoff equations. |
| title | Critical fractional Kirchhoff problems: Uniqueness and Nondegeneracy |
| topic | Analysis of PDEs 35R11, 35A15, 47G20 |
| url | https://arxiv.org/abs/2503.20277 |