| Abstract: |
| We discuss singular radially symmetric solution to the Lin-Ni-Takagi equation for a supercritical power non-linearity in dimension $N\geq 3$. We show that for any ball and any $k \geq 0$, there is a singular solution that satisfies Neumann boundary condition and oscillates at least $k$ times around the constant equilibrium. Moreover, we show that the Morse index of the singular solution is finite or infinite if the exponent is respectively larger or smaller than the Joseph--Lundgren exponent. |
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