Exact morse index computation for nodal radial solutions of Lane-Emden problems

We consider the semilinear Lane–Emden problem [Equation not available: see fulltext.]where B is the unit ball of RN, N≥ 2 , centered at the origin and 1 < p< pS, with pS= + ∞ if N= 2 and pS=N+2N-2 if N≥ 3. Our main result is to prove that in dimension N= 2 the Morse index of the least energy sign-changing radial solution up of (Ep) is exactly 12 if p is sufficiently large. As an intermediate step we compute explicitly the first eigenvalue of a limit weighted problem in RN in any dimension N≥ 2. © 2016, Springer-Verlag Berlin Heidelberg.