Extremal sign changing solutions of semilinear Dirichlet problems (Q2711939)

The author deals with the Dirichlet problem NEWLINE\[NEWLINE\begin{cases} -\Delta u=f(x,u) \quad & \text{in }\Omega\\ u=0\quad & \text{on }\partial \Omega \end{cases} NEWLINE\]NEWLINE where \(\Omega\subset \mathbb{R}^N\) is a bounded domain with smooth boundary and \(f:\Omega \times\mathbb{R} \to\mathbb{R}\) is continuous. In this note the author is interested in a special type of sign changing solution and he presents a new approach to the existence of extremal sign changing solutions.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00021].