Non existence of solutions for a slightly super-critical elliptic problem with non-power nonlinearity

Mohamed Ben Ayed; Habib Fourti

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arXiv · 2509.02140

Non existence of solutions for a slightly super-critical elliptic problem with non-power nonlinearity

Mohamed Ben Ayed·Habib Fourti

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Abstract

In this paper, we are concerned with the following elliptic equation $$ ( SC_\varepsilon ) \qquad \begin{cases} -\Delta u = |u|^{4/(n-2)}u [\ln (e+|u|)]^\varepsilon & \hbox{ in } \Omega,\\ u = 0 & \hbox{ on }\partial \Omega, \end{cases} $$ where $\Omega $ 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.

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Mohamed Ben Ayed, Habib Fourti. 2025-09-02. Non existence of solutions for a slightly super-critical elliptic problem with non-power nonlinearity. https://arxiv.org/abs/2509.02140

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