Seminar Analysis: Isabella Ianni (University of Naples II)

A Morse index formula for the Lane-Emden problem

We consider the semilinear Lane-Emden problem (E_p):

-Δu = |u|^p-1u    in  B
   u = 0            on ∂B

where B is the unit ball of R^N, N≥3, centered at the origin and 1< p < p_S, p_S=(N+2)/(N−2). We compute the Morse index of any radial solutionup of (E_p), for p sufficiently close to p_S. The proof exploits the asymptotic behavior of u_p as p→p_S and the analysis of a limit eigenvalue problem.

This is a joint work with F. De Marchis and F. Pacella

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