$\Omega$ is a open connect bounded set of $\mathbb R^n$.
\begin{align}
-\Delta u &= \lambda u \\
u|_{\partial\Omega} &=0 \\
\left.\frac{\partial u}{\partial \nu}\right|_{\partial\Omega} &=0
\end{align}
Whether this question have non-trival solution ? I mean the $\lambda$ and $u$ are not constant.
2026-03-25 14:39:41.1774449581
Eigenvalue question with Dirichlet and Neumann condition
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