We compute the Morse index m(up) of any radial solution up of the semilinear problem:where B is the unit ball of R 2 centered at the origin, α ≥ 0 is fixed and p > 1 is sufficiently large. In the case α = 0, i.e. for the Lane-Emden problem, this leads to the following Morse index formula m(up) = 4m 2 − m − 2, for p large enough, where m is the number of nodal domains of u.
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