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arXiv · 2608.15638

New sign-changing solutions to the H\'{e}non problem in dimension $2$

Francesca Gladiali·Pingping Yang
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Abstract

In this paper, we construct new sign-changing solutions for the H\'{e}non problem \begin{equation*} \begin{cases} -\Delta u= |x|^{\alpha} |u|^{p-1}u,\,\,\,\text{in}\,\,\, \Omega, \\[1mm] u=0,\,\,\,\,\,\,\text{on}\,\,\, \partial\Omega, \end{cases} \end{equation*} where $\Omega\subseteq \mathbb{R}^2$ is a bounded smooth domain containing 0, $\alpha\in\mathbb{R}$ is a positive parameter and $p$ approaches $+\infty$.

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Francesca Gladiali, Pingping Yang. 2026-08-16. New sign-changing solutions to the H\'{e}non problem in dimension $2$. https://arxiv.org/abs/2608.15638

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