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  • V článku se vyšetřuje analogie známé Courantovy věty o nodálních oblastech vlastních funkcí Laplaceova operátoru. Uvažuje se zobecnění na vlastní funkce p-laplaciánu. Za předpokladu platnosti tzv. unique continuation property je výše uvedený výsledek přenesen v plné obecnosti. Bez tohoto předpokladu je dokázán slabší odhad. (cs)
  • In this paper we consider the analogue of the Courant nodal domain theorem for the nonlinear eigenvalue problem for the p-Laplacian. In particular we prove that if $u_{\lambda_n}$ is an eigenfunction associated with the nth variational eigenvalue, $\lambda_n$, then $u_{\lambda_n}$ has at most 2n -2 nodal domain. Also, if $u_{\lambda_n}$ has n+k nodal domains, then there is another eigenfunction with at most n-k nodal domains.
  • In this paper we consider the analogue of the Courant nodal domain theorem for the nonlinear eigenvalue problem for the p-Laplacian. In particular we prove that if $u_{\lambda_n}$ is an eigenfunction associated with the nth variational eigenvalue, $\lambda_n$, then $u_{\lambda_n}$ has at most 2n -2 nodal domain. Also, if $u_{\lambda_n}$ has n+k nodal domains, then there is another eigenfunction with at most n-k nodal domains. (en)
Title
  • Zobecnění Courantovy věty o nodálních oblastech (cs)
  • On the generalization of the Courant nodal domain theorem
  • On the generalization of the Courant nodal domain theorem (en)
skos:prefLabel
  • Zobecnění Courantovy věty o nodálních oblastech (cs)
  • On the generalization of the Courant nodal domain theorem
  • On the generalization of the Courant nodal domain theorem (en)
skos:notation
  • RIV/49777513:23520/02:00000070!RIV07-GA0-23520___
http://linked.open.../vavai/riv/strany
  • 58
http://linked.open...avai/riv/aktivita
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  • P(GA201/00/0376), P(VS97156), Z(MSM 235200001)
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  • 0
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  • 656955
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  • RIV/49777513:23520/02:00000070
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  • nodal domain; p-Laplacian; Fučik spectrum; eigenvalue problem (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [A1B0407CBFC5]
http://linked.open...i/riv/nazevZdroje
  • Journal of Differential Equations
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http://linked.open...vavai/riv/projekt
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http://linked.open...iv/tvurceVysledku
  • Drábek, Pavel
  • Robinson, Stephen B.
http://linked.open...n/vavai/riv/zamer
issn
  • 0022-0396
number of pages
http://localhost/t...ganizacniJednotka
  • 23520
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