Spectral analysis of a generalized buckling problem on a ball

2016/10/16 by De Coster, Colette, Nicaise, Serge, Troestler, Christophe · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.04840

Abstract

In this paper, the spectrum of the following fourth order problem \begincases Δ² u+νu=-λΔu amp;in D₁,\newline u=∂_r u= 0 amp;on ∂ D₁, \endcases where D₁ is the unit ball in \mathbb R^N, 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 and for ν<0.

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