Extremal Solutions to Periodic Boundary Value Problem of Nabla Integrodifferential Equation of Volterra Type on Time Scales

Extremal Solutions to Periodic Boundary Value Problem of Nabla Integrodifferential Equation of Volterra Type on Time Scales

We firstly establish some new theorems on time scales, and then, by employing them together with a new comparison result and the monotone iterative technique, we show the existence of extremal solutions to the following nabla integrodifferential periodic boundary value problem: u∇(t)=f(t,u,∫0t‍g(t,s...

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Main Authors: Yunlong Shi, Junfang Zhao
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2014/205659
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spelling doaj-b3caa9f6b47c4339a47605cd1b4cfa272020-11-24T23:51:15ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/205659205659Extremal Solutions to Periodic Boundary Value Problem of Nabla Integrodifferential Equation of Volterra Type on Time ScalesYunlong Shi0Junfang Zhao1Personnel Office, China University of Geosciences, Beijing 100083, ChinaSchool of Science, China University of Geosciences, Beijing 100083, ChinaWe firstly establish some new theorems on time scales, and then, by employing them together with a new comparison result and the monotone iterative technique, we show the existence of extremal solutions to the following nabla integrodifferential periodic boundary value problem: u∇(t)=f(t,u,∫0t‍g(t,s)∇s),  t∈[0,a]T,  u(0)=u(ρ(a)), where T is a time scale.http://dx.doi.org/10.1155/2014/205659
collection DOAJ
language English
format Article
sources DOAJ
author Yunlong Shi
Junfang Zhao
spellingShingle Yunlong Shi
Junfang Zhao
Extremal Solutions to Periodic Boundary Value Problem of Nabla Integrodifferential Equation of Volterra Type on Time Scales
Discrete Dynamics in Nature and Society
author_facet Yunlong Shi
Junfang Zhao
author_sort Yunlong Shi
title Extremal Solutions to Periodic Boundary Value Problem of Nabla Integrodifferential Equation of Volterra Type on Time Scales
title_short Extremal Solutions to Periodic Boundary Value Problem of Nabla Integrodifferential Equation of Volterra Type on Time Scales
title_full Extremal Solutions to Periodic Boundary Value Problem of Nabla Integrodifferential Equation of Volterra Type on Time Scales
title_fullStr Extremal Solutions to Periodic Boundary Value Problem of Nabla Integrodifferential Equation of Volterra Type on Time Scales
title_full_unstemmed Extremal Solutions to Periodic Boundary Value Problem of Nabla Integrodifferential Equation of Volterra Type on Time Scales
title_sort extremal solutions to periodic boundary value problem of nabla integrodifferential equation of volterra type on time scales
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2014-01-01
description We firstly establish some new theorems on time scales, and then, by employing them together with a new comparison result and the monotone iterative technique, we show the existence of extremal solutions to the following nabla integrodifferential periodic boundary value problem: u∇(t)=f(t,u,∫0t‍g(t,s)∇s),  t∈[0,a]T,  u(0)=u(ρ(a)), where T is a time scale.
url http://dx.doi.org/10.1155/2014/205659
work_keys_str_mv AT yunlongshi extremalsolutionstoperiodicboundaryvalueproblemofnablaintegrodifferentialequationofvolterratypeontimescales
AT junfangzhao extremalsolutionstoperiodicboundaryvalueproblemofnablaintegrodifferentialequationofvolterratypeontimescales
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