Periodic boundary value problems on time scales

Periodic boundary value problems on time scales

We extend the results concerning periodic boundary value problems from the continuous calculus to time scales. First we use the Schauder fixed point theorem and the concept of lower and upper solutions to prove the existence of the solutions and then we investigate a monotone iterative method which...

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Main Author: Petr Stehlík
Format: Article
Language:English
Published: SpringerOpen 2005-03-01
Series:Advances in Difference Equations
Online Access:http://dx.doi.org/10.1155/ADE.2005.81
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spelling doaj-3c0ce3289eff4b8abf34a1e1aeecfd582020-11-24T21:15:30ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472005-03-0120051819210.1155/ADE.2005.81Periodic boundary value problems on time scalesPetr StehlíkWe extend the results concerning periodic boundary value problems from the continuous calculus to time scales. First we use the Schauder fixed point theorem and the concept of lower and upper solutions to prove the existence of the solutions and then we investigate a monotone iterative method which could generate some of them. Since this method does not work on each time scale, a condition containing a Lipschitz constant of right-hand side function and the supremum of the graininess function is introduced.http://dx.doi.org/10.1155/ADE.2005.81
collection DOAJ
language English
format Article
sources DOAJ
author Petr Stehlík
spellingShingle Petr Stehlík
Periodic boundary value problems on time scales
Advances in Difference Equations
author_facet Petr Stehlík
author_sort Petr Stehlík
title Periodic boundary value problems on time scales
title_short Periodic boundary value problems on time scales
title_full Periodic boundary value problems on time scales
title_fullStr Periodic boundary value problems on time scales
title_full_unstemmed Periodic boundary value problems on time scales
title_sort periodic boundary value problems on time scales
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1839
1687-1847
publishDate 2005-03-01
description We extend the results concerning periodic boundary value problems from the continuous calculus to time scales. First we use the Schauder fixed point theorem and the concept of lower and upper solutions to prove the existence of the solutions and then we investigate a monotone iterative method which could generate some of them. Since this method does not work on each time scale, a condition containing a Lipschitz constant of right-hand side function and the supremum of the graininess function is introduced.
url http://dx.doi.org/10.1155/ADE.2005.81
work_keys_str_mv AT petrstehl237k periodicboundaryvalueproblemsontimescales
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