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Description
  • Uvažujeme variační nerovnice s vícedimenzionálním parametrem na uzavřených konvexních množinách jistého typu (obecně ne na kuželech) a ukazujeme lokální $C^k$-hladkou závislost jejich řešení na parametru. Základní myšlenkou je za jistých předpokladů ukázat, že variační nerovnice je na okolí daného řešení ekvivalentní s jistou rovnicí, na kterou je použita věta o implicitní funkci. Výsledek je aplikován na model nosníku, který je jednostranně podepřen v různých výškách v konečně mnoha bodech a na závislost Nashova ekvilibria na parametrech. (cs)
  • Variational inequalities on closed convex sets of a certain type (not cones in general) with a multidimensional parameter are considered, and the local $C^k$-smooth dependence of their solutions on the parameter is proved. The basic idea is to show that under some assumptions, the variational inequality is in a neighbourhood of a given solution equivalent to an equation for which Implicit Function Theorem can be used. The result is applied to a model of a beam unilaterally supported by a finite number of fixed obstacles in different hights, and to Nash equilibria with parameters.
  • Variational inequalities on closed convex sets of a certain type (not cones in general) with a multidimensional parameter are considered, and the local $C^k$-smooth dependence of their solutions on the parameter is proved. The basic idea is to show that under some assumptions, the variational inequality is in a neighbourhood of a given solution equivalent to an equation for which Implicit Function Theorem can be used. The result is applied to a model of a beam unilaterally supported by a finite number of fixed obstacles in different hights, and to Nash equilibria with parameters. (en)
Title
  • Smooth dependence on parameters of solutions to variational inequalities
  • Smooth dependence on parameters of solutions to variational inequalities (en)
  • Hladká závislost řešení variačních nerovnic na parametrech (cs)
skos:prefLabel
  • Smooth dependence on parameters of solutions to variational inequalities
  • Smooth dependence on parameters of solutions to variational inequalities (en)
  • Hladká závislost řešení variačních nerovnic na parametrech (cs)
skos:notation
  • RIV/67985840:_____/05:00022023!RIV06-AV0-67985840
http://linked.open.../vavai/riv/strany
  • 849;861
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(IAA1019202), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika
  • 5
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 543185
http://linked.open...ai/riv/idVysledku
  • RIV/67985840:_____/05:00022023
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • multiparameter variational inequality; smooth dependence on parameters; implicit function theorem (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV
  • [23F112A18A96]
http://linked.open...i/riv/nazevZdroje
  • Nonlinear Analysis, Theory, Methods and Applications
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 62
http://linked.open...iv/tvurceVysledku
  • Eisner, Jan
  • Kučera, Milan
  • Recke, L.
http://linked.open...n/vavai/riv/zamer
issn
  • 0362-546X
number of pages
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