01 Mar 2017
14:15  - 15:15

Spiegelgasse 1, Lecture Room 0.003

Seminar Analysis: Isabella Ianni (University of Naples II)

A Morse index formula for the Lane-Emden problem

 

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

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

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

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


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