We consider the following Dirichlet problem

$\left\{ \begin{matrix} -\Delta u=\lambda f(u)\ \ \ \ \text{in}\ \Omega \\ u=0\ \ \ \ \ \ \ \ \ \ \ \ \ \text{on}\ \partial \Omega \\\end{matrix} \right.,\ \ \ \ \ \ \ \left( \mathcal{P}_{f}^{\lambda } \right)$

中文翻译：

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最小解的渐近行为 \ begin {document} $-\ Delta u = \ lambda f（u）$ \ end {document} 如 \ begin {document} $ \ lambda \ to- \ infty $ \ end {document}

我们考虑以下狄利克雷问题

$ \ left \ {\ begin {matrix}-\ Delta u = \ lambda f（u）\ \ \ \ \ text {in} \ \ Omega \\ u = 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ text {on} \ \ partial \ Omega \\\ end {matrix} \ right。，\ \ \ \ \ \ \ \ left（\ mathcal {P} _ {f} ^ {\ lambda} \ right）$