Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations

Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations

We prove existence and uniqueness results in the presence of coupled lower and upper solutions for the general nth problem in time scales with linear dependence on the ith Δ-derivatives for i=1,2,…,n, together with antiperiodic boundary value conditions. Here the nonlinear right-hand side of...

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Main Authors: Dolores R. Vivero, Alberto Cabada
Format: Article
Language:English
Published: SpringerOpen 2004-12-01
Series:Advances in Difference Equations
Online Access:http://dx.doi.org/10.1155/S1687183904310022
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spelling doaj-246aaa5d35974cc0bf196b7b23b4c8ac2020-11-25T01:54:33ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472004-12-012004429131010.1155/S1687183904310022Existence and uniqueness of solutions of higher-order antiperiodic dynamic equationsDolores R. ViveroAlberto CabadaWe prove existence and uniqueness results in the presence of coupled lower and upper solutions for the general nth problem in time scales with linear dependence on the ith Δ-derivatives for i=1,2,…,n, together with antiperiodic boundary value conditions. Here the nonlinear right-hand side of the equation is defined by a function f(t,x) which is rd-continuous in t and continuous in x uniformly in t. To do that, we obtain the expression of the Green's function of a related linear operator in the space of the antiperiodic functions.http://dx.doi.org/10.1155/S1687183904310022
collection DOAJ
language English
format Article
sources DOAJ
author Dolores R. Vivero
Alberto Cabada
spellingShingle Dolores R. Vivero
Alberto Cabada
Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations
Advances in Difference Equations
author_facet Dolores R. Vivero
Alberto Cabada
author_sort Dolores R. Vivero
title Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations
title_short Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations
title_full Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations
title_fullStr Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations
title_full_unstemmed Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations
title_sort existence and uniqueness of solutions of higher-order antiperiodic dynamic equations
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1839
1687-1847
publishDate 2004-12-01
description We prove existence and uniqueness results in the presence of coupled lower and upper solutions for the general nth problem in time scales with linear dependence on the ith Δ-derivatives for i=1,2,…,n, together with antiperiodic boundary value conditions. Here the nonlinear right-hand side of the equation is defined by a function f(t,x) which is rd-continuous in t and continuous in x uniformly in t. To do that, we obtain the expression of the Green's function of a related linear operator in the space of the antiperiodic functions.
url http://dx.doi.org/10.1155/S1687183904310022
work_keys_str_mv AT doloresrvivero existenceanduniquenessofsolutionsofhigherorderantiperiodicdynamicequations
AT albertocabada existenceanduniquenessofsolutionsofhigherorderantiperiodicdynamicequations
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