Normalized solutions to polyharmonic equations with Hardy-type potentials and exponential critical nonlinearities
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| Format: | Preprint |
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2024
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| _version_ | 1866908594771853312 |
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| author | Bieganowski, Bartosz Miyagaki, Olímpio Hiroshi Schino, Jacopo |
| author_facet | Bieganowski, Bartosz Miyagaki, Olímpio Hiroshi Schino, Jacopo |
| contents | Via a constrained minimization, we find a solution $(λ,u)$ to the problem \begin{equation*} \begin{cases} (-Δ)^m u+\fracμ{|x|^{2m}}u + λu = ηu^3 + g(u)\\ \int_{\mathbb{R}^{2m}} u^2 \, dx = ρ\end{cases} \end{equation*} with $1 \le m \in \mathbb{N}$, $μ,η\ge 0$, $ρ> 0$, and $g$ having exponential critical growth at infinity and mass supercritical growth at zero. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_05885 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normalized solutions to polyharmonic equations with Hardy-type potentials and exponential critical nonlinearities Bieganowski, Bartosz Miyagaki, Olímpio Hiroshi Schino, Jacopo Analysis of PDEs Via a constrained minimization, we find a solution $(λ,u)$ to the problem \begin{equation*} \begin{cases} (-Δ)^m u+\fracμ{|x|^{2m}}u + λu = ηu^3 + g(u)\\ \int_{\mathbb{R}^{2m}} u^2 \, dx = ρ\end{cases} \end{equation*} with $1 \le m \in \mathbb{N}$, $μ,η\ge 0$, $ρ> 0$, and $g$ having exponential critical growth at infinity and mass supercritical growth at zero. |
| title | Normalized solutions to polyharmonic equations with Hardy-type potentials and exponential critical nonlinearities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.05885 |