Spectral analysis of a generalized buckling problem on a ball

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).