| Abstract: |
| In this talk I will give a brief overview of some results concerning the existence of positive multi-peak solutions with Dirichlet boundary conditions for a class of slightly subcritical or slightly supercritical elliptic problems. I will also present some recent results, obtained in collaboration with Giuseppe Rago and Giusi Vaira, on arbitrary dimensional annuli.
By exploiting the explicit form of the Green function and the Robin function for the annulus, we prove that, in the slightly subcritical case, the annulus must become thinner and thinner as the number of peaks increases, whereas, in the slightly supercritical case, the inner hole of the annulus must be very small. |
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