On variational eigenvalues of the p-Laplacian which are not of Ljusternik�Schnirelmann type
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Autores: Pavel Drábek, Peter Takác
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 81, Nº 3, 2010, págs. 625-649
- Idioma: inglés
- DOI: 10.1112/jlms/jdq006
- Enlaces
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Resumen
In this paper we demonstrate the fact that the famous Ljusternik�Schnirelmann characterization of some eigenvalues of nonlinear elliptic problems (by a minimax formula) has a global variational character. Indeed, we show that, for some homogeneous quasilinear elliptic eigenvalue problems, there are variational eigenvalues other than those of the Ljusternik�Schnirelmann type. In contrast, these eigenvalues have a local variational character. Such a phenomenon does not occur in typical linear elliptic eigenvalue problems, owing to the Courant�Fischer theorem which is the linear analogue and predecessor of the Ljusternik�Schnirelmann theory.
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