Abstract
<p style='text-indent:20px;'>In this survey we discuss old and new results on the number of critical points of solutions of the problem</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE0.1"> \begin{document}$ \begin{equation} \begin{cases} -\Delta u = f(u)&in\ \Omega\\ u = 0&on\ \partial \Omega \end{cases} \;\;\;\;\;\;\;\;(0.1)\end{equation} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ \Omega\subset \mathbb{R}^N $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M2">\begin{document}$ N\ge2 $\end{document}</tex-math></inline-formula> is a smooth bounded domain. Both cases where <inline-formula><tex-math id="M3">\begin{document}$ u $\end{document}</tex-math></inline-formula> is a positive or nodal solution will be considered.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
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