Spectral analysis of a generalized buckling problem on a ball

Colette De Coster (1) , Serge Nicaise (1) , Christophe Troestler (2)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
2 UMons - Université de Mons

In this paper, the spectrum of the following fourth order problem (Formula Presented.)where D1 is the unit ball in RN, is determined for ν< 0 as well as the nodal properties of the corresponding eigenfunctions. In particular, we show that the first eigenvalue is simple and that the corresponding eigenfunction is radial and (up to a multiplicative factor) positive and decreasing with respect to the radius. This completes earlier results obtained for ν⩾ 0 (see Coster et al. in Positivity 19:843–875, 2015) and for ν< 0 (see Laurençot and Walker in J Anal Math 127:69–89, 2014).

Mots clés: Buckling problem; Spectral analysis; Properties of eigenfunctions

Domaines: Mathématiques [math]

Colette De Coster, Serge Nicaise, Christophe Troestler. Spectral analysis of a generalized buckling problem on a ball. Positivity, 2017, 21 (4), pp.1319-1340. ⟨10.1007/s11117-017-0469-x⟩. ⟨hal-03163589⟩