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  • 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.
  • 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. (en)
Title
  • On variational eigenvalues of the p-Laplacian which are not of Ljusternik-Schnirelmann type
  • On variational eigenvalues of the p-Laplacian which are not of Ljusternik-Schnirelmann type (en)
skos:prefLabel
  • On variational eigenvalues of the p-Laplacian which are not of Ljusternik-Schnirelmann type
  • On variational eigenvalues of the p-Laplacian which are not of Ljusternik-Schnirelmann type (en)
skos:notation
  • RIV/49777513:23520/10:00503407!RIV11-MSM-23520___
http://linked.open...avai/riv/aktivita
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  • P(MEB100902), Z(MSM4977751301)
http://linked.open...iv/cisloPeriodika
  • 3
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http://linked.open...aciTvurceVysledku
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  • 276951
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  • RIV/49777513:23520/10:00503407
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  • variational eigenvalues; p-Lapacian; Ljusternik-Schnirelmann method (en)
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http://linked.open...odStatuVydavatele
  • GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV
  • [A895A71A9798]
http://linked.open...i/riv/nazevZdroje
  • JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
http://linked.open...in/vavai/riv/obor
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http://linked.open...v/svazekPeriodika
  • 81
http://linked.open...iv/tvurceVysledku
  • Drábek, Pavel
  • Takáč, Peter
http://linked.open...ain/vavai/riv/wos
  • 000278819000007
http://linked.open...n/vavai/riv/zamer
issn
  • 0024-6107
number of pages
http://localhost/t...ganizacniJednotka
  • 23520
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