[en] spectrum; [en] 4th order PDE; [en] eigenvalues
Abstract :
[en] In this paper, the spectrum of the following fourth order problem
Δ²u + ν u = -λ Δu in D₁,
u = ∂ᵣu = 0 on ∂D₁,
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 and for ν<0.
Research center :
CREMMI - Modélisation mathématique et informatique
Disciplines :
Computer science Mathematics
Author, co-author :
Troestler, Christophe ; Université de Mons > Faculté des Sciences > Service d'Analyse numérique
De Coster, Colette
Nicaise, Serge
Language :
English
Title :
Spectral analysis of a generalized buckling problem on a ball
Publication date :
14 January 2017
Journal title :
Positivity
ISSN :
1385-1292
Publisher :
Birkhäuser, Switzerland
Volume :
21
Issue :
4
Pages :
1319-1340
Peer reviewed :
Peer reviewed
Research unit :
S835 - Analyse numérique
Research institute :
R150 - Institut de Recherche sur les Systèmes Complexes
