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- Title
Nodal properties of eigenfunctions of a generalized buckling problem on balls.
- Authors
De Coster, Colette; Nicaise, Serge; Troestler, Christophe
- Abstract
In this paper we are interested in the following fourth order eigenvalue problem coming from the buckling of thin films on liquid substrates: where $$B_1$$ is the unit ball in $${\mathbb R}^N$$ . When $$\kappa > 0$$ is small, we show that the first eigenvalue is simple and the first eigenfunction, which gives the shape of the film for small displacements, is positive. However, when $$\kappa $$ increases, we establish that the first eigenvalue is not always simple and the first eigenfunction may change sign. More precisely, for any $$\kappa \in \mathopen ]0,+\infty \mathclose [$$ , we give the exact multiplicity of the first eigenvalue and the number of nodal regions of the first eigenfunction.
- Subjects
EIGENFUNCTIONS; MECHANICAL buckling; MOLECULAR shapes; NODAL planes; EIGENVALUES; MULTIPLICITY (Mathematics)
- Publication
Positivity, 2015, Vol 19, Issue 4, p843
- ISSN
1385-1292
- Publication type
Article
- DOI
10.1007/s11117-015-0331-y