Abstract
We consider the semilinear Lane–Emden problem:(Ep){−Δu=|u|p−1u in Bu=0 on ∂B where B is the unit ball of RN, N≥3, centered at the origin and 1<p<pS, pS=N+2N−2.We prove that for any radial solution up of (Ep) with m nodal domains its Morse index m(up) is given by the formulam(up)=m+N(m−1) if p is sufficiently close to pS.
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