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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2512.18663 |
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| _version_ | 1866914213044158464 |
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| author | Liu, Zhongyuan Tian, Shuying Xie, Huafei Yang, Pingping |
| author_facet | Liu, Zhongyuan Tian, Shuying Xie, Huafei Yang, Pingping |
| contents | In this paper, we are concerned with qualitative properties of multi-peak solutions of the following nonlinear Schrödinger equations \begin{equation*} -Δu+V(x)u= u^{p-\varepsilon},\,\,\,u>0,\,\,\,\text{in}\,\,\,\mathbb{R}^N, \end{equation*} where $V(x)$ is a nonnegative continuous function, $\varepsilon>0$, $p=\frac{N+2}{N-2}$, $N\geq6$. The existence of multi-peak solutions has been obtained by Cao et al. (Calc. Var. Partial Differential Equations, 64: 139, 2025). The main objective in this paper is to establish the local uniqueness and Morse index of the multi-peak solutions in \cite{CLl1} provided that $V(x)$ possesses $k$ non-degenerate critical points by using the blow-up analysis based on Pohozaev identities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Qualitative analysis of multi-peak solutions for Nonlinear Schrödinger equations with nearly critical Sobolev exponents Liu, Zhongyuan Tian, Shuying Xie, Huafei Yang, Pingping Analysis of PDEs Category Theory In this paper, we are concerned with qualitative properties of multi-peak solutions of the following nonlinear Schrödinger equations \begin{equation*} -Δu+V(x)u= u^{p-\varepsilon},\,\,\,u>0,\,\,\,\text{in}\,\,\,\mathbb{R}^N, \end{equation*} where $V(x)$ is a nonnegative continuous function, $\varepsilon>0$, $p=\frac{N+2}{N-2}$, $N\geq6$. The existence of multi-peak solutions has been obtained by Cao et al. (Calc. Var. Partial Differential Equations, 64: 139, 2025). The main objective in this paper is to establish the local uniqueness and Morse index of the multi-peak solutions in \cite{CLl1} provided that $V(x)$ possesses $k$ non-degenerate critical points by using the blow-up analysis based on Pohozaev identities. |
| title | Qualitative analysis of multi-peak solutions for Nonlinear Schrödinger equations with nearly critical Sobolev exponents |
| topic | Analysis of PDEs Category Theory |
| url | https://arxiv.org/abs/2512.18663 |