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

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

    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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