Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)

Third order linear homogeneous differential and recurrence equations with constant coefficients are considered. We take the both equations with the same characteristic equation. We show that these equations (differential and recurrence) can have solutions with different properties concerning oscilla...

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Main Authors:	Jarosław Mikołajski, Ewa Schmeidel
Format:	Article
Language:	English
Published:	AGH Univeristy of Science and Technology Press 2006-01-01
Series:	Opuscula Mathematica
Subjects:	differential equation recurrence linear third order oscillatory solution bounded solution
Online Access:	http://www.opuscula.agh.edu.pl/vol26/2/art/opuscula_math_2624.pdf

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spelling	doaj-de314282e4b742dfaa33e8bad53dd2b12020-11-25T01:47:09ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742006-01-012623433492624Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)Jarosław Mikołajski0Ewa Schmeidel1Poznań University of Technology, Institute of Mathematics, Faculty of Electrical Engineering, ul. Piotrowo 3a, 60-965 Poznań, PolandPoznań University of Technology, Institute of Mathematics, Faculty of Electrical Engineering, ul. Piotrowo 3a, 60-965 Poznań, PolandThird order linear homogeneous differential and recurrence equations with constant coefficients are considered. We take the both equations with the same characteristic equation. We show that these equations (differential and recurrence) can have solutions with different properties concerning oscillation and boundedness. Especially the numbers of suitable types of solutions taken out from fundamental sets are presented. We give conditions under which the asymptotic properties considered are the same for the both equations.http://www.opuscula.agh.edu.pl/vol26/2/art/opuscula_math_2624.pdfdifferential equationrecurrencelinearthird orderoscillatory solutionbounded solution
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jarosław Mikołajski Ewa Schmeidel
spellingShingle	Jarosław Mikołajski Ewa Schmeidel Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients) Opuscula Mathematica differential equation recurrence linear third order oscillatory solution bounded solution
author_facet	Jarosław Mikołajski Ewa Schmeidel
author_sort	Jarosław Mikołajski
title	Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)
title_short	Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)
title_full	Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)
title_fullStr	Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)
title_full_unstemmed	Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)
title_sort	comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)
publisher	AGH Univeristy of Science and Technology Press
series	Opuscula Mathematica
issn	1232-9274
publishDate	2006-01-01
description	Third order linear homogeneous differential and recurrence equations with constant coefficients are considered. We take the both equations with the same characteristic equation. We show that these equations (differential and recurrence) can have solutions with different properties concerning oscillation and boundedness. Especially the numbers of suitable types of solutions taken out from fundamental sets are presented. We give conditions under which the asymptotic properties considered are the same for the both equations.
topic	differential equation recurrence linear third order oscillatory solution bounded solution
url	http://www.opuscula.agh.edu.pl/vol26/2/art/opuscula_math_2624.pdf
work_keys_str_mv	AT jarosławmikołajski comparisonofpropertiesofsolutionsofdifferentialequationsandrecurrenceequationswiththesamecharacteristicequationonexampleofthirdorderlinearequationswithconstantcoefficients AT ewaschmeidel comparisonofpropertiesofsolutionsofdifferentialequationsandrecurrenceequationswiththesamecharacteristicequationonexampleofthirdorderlinearequationswithconstantcoefficients
_version_	1725015914398613504

Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)

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