Non existence of solutions for a slightly super-critical elliptic problem with non-power nonlinearity
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915474757910528 |
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| author | Ayed, Mohamed Ben Fourti, Habib |
| author_facet | Ayed, Mohamed Ben Fourti, Habib |
| contents | In this paper, we are concerned with the following elliptic equation $$ ( SC_\varepsilon ) \qquad
\begin{cases} -Δu = |u|^{4/(n-2)}u [\ln (e+|u|)]^\varepsilon & \hbox{ in } Ω,\\ u = 0 & \hbox{ on }\partial Ω, \end{cases} $$ where $Ω$ is a smooth bounded open domain in $\mathbb{R}^n, \ n\geq 3$ and $\varepsilon >0$. In Comm. Contemp. Math. (2003), Ben Ayed et al. showed that the slightly supercritical usual elliptic problem has no single peaked solution. Here we extend their result for problem $( SC_\varepsilon )$ when $\varepsilon$ is small enough, and that by assuming a new assumption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02140 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non existence of solutions for a slightly super-critical elliptic problem with non-power nonlinearity Ayed, Mohamed Ben Fourti, Habib Analysis of PDEs In this paper, we are concerned with the following elliptic equation $$ ( SC_\varepsilon ) \qquad \begin{cases} -Δu = |u|^{4/(n-2)}u [\ln (e+|u|)]^\varepsilon & \hbox{ in } Ω,\\ u = 0 & \hbox{ on }\partial Ω, \end{cases} $$ where $Ω$ is a smooth bounded open domain in $\mathbb{R}^n, \ n\geq 3$ and $\varepsilon >0$. In Comm. Contemp. Math. (2003), Ben Ayed et al. showed that the slightly supercritical usual elliptic problem has no single peaked solution. Here we extend their result for problem $( SC_\varepsilon )$ when $\varepsilon$ is small enough, and that by assuming a new assumption. |
| title | Non existence of solutions for a slightly super-critical elliptic problem with non-power nonlinearity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.02140 |