### Electronic Research Archive

2021, Issue 6: 4215-4228. doi: 10.3934/era.2021080
Special Issues

# On the number of critical points of solutions of semilinear elliptic equations

• Received: 01 July 2021 Revised: 01 August 2021 Published: 08 October 2021
• 35B05, 35B06, 35B09

• In this survey we discuss old and new results on the number of critical points of solutions of the problem

$$$\begin{cases} -\Delta u = f(u)&in\ \Omega\\ u = 0&on\ \partial \Omega \end{cases} \;\;\;\;\;\;\;\;(0.1)$$$

where $\Omega\subset \mathbb{R}^N$ with $N\ge2$ is a smooth bounded domain. Both cases where $u$ is a positive or nodal solution will be considered.

Citation: Massimo Grossi. On the number of critical points of solutions of semilinear elliptic equations[J]. Electronic Research Archive, 2021, 29(6): 4215-4228. doi: 10.3934/era.2021080

### Related Papers:

• In this survey we discuss old and new results on the number of critical points of solutions of the problem

$$$\begin{cases} -\Delta u = f(u)&in\ \Omega\\ u = 0&on\ \partial \Omega \end{cases} \;\;\;\;\;\;\;\;(0.1)$$$

where $\Omega\subset \mathbb{R}^N$ with $N\ge2$ is a smooth bounded domain. Both cases where $u$ is a positive or nodal solution will be considered.

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