Ricerc@Sapienza

We compute the Morse index of 1-spike solutions of the semilinear elliptic problem
()
where is a smooth bounded domain and is sufficiently large.

When Ω is convex, our result, combined with the characterization in [21], a result in [40] and with recent uniform estimates in [37], gives the uniqueness of the solution to (), for p large. This proves, in dimension two and for p large, a longstanding conjecture.