New type of solutions for Schrödinger equations with critical growth
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914646879895552 |
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| author | Gao, Yuan Guo, Yuxia |
| author_facet | Gao, Yuan Guo, Yuxia |
| contents | We consider the following nonlinear Schrödinger equations with critical growth: \begin{equation} - Δu + V(|y|)u=u^{\frac{N+2}{N-2}},\quad u>0 \ \ \mbox{in} \ \mathbb {R}^N, \end{equation} where $V(|y|)$ is a bounded positive radial function in $C^1$, $N\ge 5$. By using a finite reduction argument, we show that if $r^2V(r)$ has either an isolated local maximum or an isolated minimum at $r_0>0$ with $V(r_0)>0$, there exists infinitely many non-radial large energy solutions which are invariant under some sub-groups of $O(3)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_11111 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New type of solutions for Schrödinger equations with critical growth Gao, Yuan Guo, Yuxia Analysis of PDEs Functional Analysis 35A01, 35B33, 35B38 We consider the following nonlinear Schrödinger equations with critical growth: \begin{equation} - Δu + V(|y|)u=u^{\frac{N+2}{N-2}},\quad u>0 \ \ \mbox{in} \ \mathbb {R}^N, \end{equation} where $V(|y|)$ is a bounded positive radial function in $C^1$, $N\ge 5$. By using a finite reduction argument, we show that if $r^2V(r)$ has either an isolated local maximum or an isolated minimum at $r_0>0$ with $V(r_0)>0$, there exists infinitely many non-radial large energy solutions which are invariant under some sub-groups of $O(3)$. |
| title | New type of solutions for Schrödinger equations with critical growth |
| topic | Analysis of PDEs Functional Analysis 35A01, 35B33, 35B38 |
| url | https://arxiv.org/abs/2401.11111 |