About: On the periodic motion of one-dimensional oscillator between two elastic walls

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We investigate the periodic solutions of a one-dimensional nonlinear pendulum $y'' + \delta y' + k \sin y + k_{1}(y - r_{1})^{+} - k_{2}(y + r_{2})^{-} = f$, where $y^{+}:=\max\{y,0\}$ and $y^{-}:=\max\{-y,0\}$. The pendulum is located between two one-sided springs with stiffnesses $k_{1}$ and $k_{2}$ in distances $r_{1}$ and $r_{2}$. For the first approximation, we investigate the simplified model without damping ($\delta = 0$) and with zero right-hand side $y'' + k y + k_{1}(y - r_{1})^{+} - k_{2}(y + r_{2})^{-} = 0$ together with periodic condition $y(t) = y(t+T)$. In the symmetric case of $r_{1} = r_{2}$ and $k_{1} = k_{2}$, we give the full and precise description of the solution set of the simplified problem with respect to its parameters. We prove the existence of multiple solutions and moreover, we provide the qualitative properties of the corresponding solution diagram. Finally, we reconstruct the solution diagram for the simplified problem also in the case of genera We investigate the periodic solutions of a one-dimensional nonlinear pendulum $y'' + \delta y' + k \sin y + k_{1}(y - r_{1})^{+} - k_{2}(y + r_{2})^{-} = f$, where $y^{+}:=\max\{y,0\}$ and $y^{-}:=\max\{-y,0\}$. The pendulum is located between two one-sided springs with stiffnesses $k_{1}$ and $k_{2}$ in distances $r_{1}$ and $r_{2}$. For the first approximation, we investigate the simplified model without damping ($\delta = 0$) and with zero right-hand side $y'' + k y + k_{1}(y - r_{1})^{+} - k_{2}(y + r_{2})^{-} = 0$ together with periodic condition $y(t) = y(t+T)$. In the symmetric case of $r_{1} = r_{2}$ and $k_{1} = k_{2}$, we give the full and precise description of the solution set of the simplified problem with respect to its parameters. We prove the existence of multiple solutions and moreover, we provide the qualitative properties of the corresponding solution diagram. Finally, we reconstruct the solution diagram for the simplified problem also in the case of genera (en)
Title	On the periodic motion of one-dimensional oscillator between two elastic walls On the periodic motion of one-dimensional oscillator between two elastic walls (en)
skos:prefLabel	On the periodic motion of one-dimensional oscillator between two elastic walls On the periodic motion of one-dimensional oscillator between two elastic walls (en)
skos:notation	RIV/49777513:23520/09:00501684!RIV10-MSM-23520___
http://linked.open...avai/riv/aktivita	S Z
http://linked.open...avai/riv/aktivity	S, Z(MSM4977751301)
http://linked.open...iv/cisloPeriodika	12
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Nečesal, Petr
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Západočeská univerzita v Plzni / Fakulta aplikovaných věd
http://linked.open...dnocenehoVysledku	331564
http://linked.open...ai/riv/idVysledku	RIV/49777513:23520/09:00501684
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Fučík spectrum; asymmetric nonlinearities; multiple periodic solutions (en)
http://linked.open.../riv/klicoveSlovo	multiple periodic solutions Fučík spectrum asymmetric nonlinearities
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[5AF17DF2923D]
http://linked.open...i/riv/nazevZdroje	Journal of Interdisciplinary Mathematics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	2009
http://linked.open...iv/tvurceVysledku	Nečesal, Petr Babováková, Jana
http://linked.open...n/vavai/riv/zamer	Spojité a diskrétní matematické struktury a vývoj odpovídajících metod jejich zkoumání
issn	0972-0502
number of pages	12 (xsd:int)
http://localhost/t...ganizacniJednotka	23520

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