Asymptotic Behavior of Solutions of Higher-Order Dynamic Equations on Time Scales
<p/> <p>We investigate the asymptotic behavior of solutions of the following higher-order dynamic equation <inline-formula><graphic file="1687-1847-2011-237219-i1.gif"/></inline-formula>, on an arbitrary time scale <inline-formula><graphic file="...
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doaj-a981100bf28b45ad9d3fa472865e07a62020-11-24T21:07:12ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472011-01-0120111237219Asymptotic Behavior of Solutions of Higher-Order Dynamic Equations on Time ScalesXi HongjianSun TaixiangPeng Xiaofeng<p/> <p>We investigate the asymptotic behavior of solutions of the following higher-order dynamic equation <inline-formula><graphic file="1687-1847-2011-237219-i1.gif"/></inline-formula>, on an arbitrary time scale <inline-formula><graphic file="1687-1847-2011-237219-i2.gif"/></inline-formula>, where the function <inline-formula><graphic file="1687-1847-2011-237219-i3.gif"/></inline-formula> is defined on <inline-formula><graphic file="1687-1847-2011-237219-i4.gif"/></inline-formula>. We give sufficient conditions under which every solution <inline-formula><graphic file="1687-1847-2011-237219-i5.gif"/></inline-formula> of this equation satisfies one of the following conditions: (1) <inline-formula><graphic file="1687-1847-2011-237219-i6.gif"/></inline-formula>; (2) there exist constants <inline-formula><graphic file="1687-1847-2011-237219-i7.gif"/></inline-formula> with <inline-formula><graphic file="1687-1847-2011-237219-i8.gif"/></inline-formula>, such that <inline-formula><graphic file="1687-1847-2011-237219-i9.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1847-2011-237219-i10.gif"/></inline-formula><inline-formula><graphic file="1687-1847-2011-237219-i11.gif"/></inline-formula> are as in Main Results.</p> http://www.advancesindifferenceequations.com/content/2011/237219 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Xi Hongjian Sun Taixiang Peng Xiaofeng |
spellingShingle |
Xi Hongjian Sun Taixiang Peng Xiaofeng Asymptotic Behavior of Solutions of Higher-Order Dynamic Equations on Time Scales Advances in Difference Equations |
author_facet |
Xi Hongjian Sun Taixiang Peng Xiaofeng |
author_sort |
Xi Hongjian |
title |
Asymptotic Behavior of Solutions of Higher-Order Dynamic Equations on Time Scales |
title_short |
Asymptotic Behavior of Solutions of Higher-Order Dynamic Equations on Time Scales |
title_full |
Asymptotic Behavior of Solutions of Higher-Order Dynamic Equations on Time Scales |
title_fullStr |
Asymptotic Behavior of Solutions of Higher-Order Dynamic Equations on Time Scales |
title_full_unstemmed |
Asymptotic Behavior of Solutions of Higher-Order Dynamic Equations on Time Scales |
title_sort |
asymptotic behavior of solutions of higher-order dynamic equations on time scales |
publisher |
SpringerOpen |
series |
Advances in Difference Equations |
issn |
1687-1839 1687-1847 |
publishDate |
2011-01-01 |
description |
<p/> <p>We investigate the asymptotic behavior of solutions of the following higher-order dynamic equation <inline-formula><graphic file="1687-1847-2011-237219-i1.gif"/></inline-formula>, on an arbitrary time scale <inline-formula><graphic file="1687-1847-2011-237219-i2.gif"/></inline-formula>, where the function <inline-formula><graphic file="1687-1847-2011-237219-i3.gif"/></inline-formula> is defined on <inline-formula><graphic file="1687-1847-2011-237219-i4.gif"/></inline-formula>. We give sufficient conditions under which every solution <inline-formula><graphic file="1687-1847-2011-237219-i5.gif"/></inline-formula> of this equation satisfies one of the following conditions: (1) <inline-formula><graphic file="1687-1847-2011-237219-i6.gif"/></inline-formula>; (2) there exist constants <inline-formula><graphic file="1687-1847-2011-237219-i7.gif"/></inline-formula> with <inline-formula><graphic file="1687-1847-2011-237219-i8.gif"/></inline-formula>, such that <inline-formula><graphic file="1687-1847-2011-237219-i9.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1847-2011-237219-i10.gif"/></inline-formula><inline-formula><graphic file="1687-1847-2011-237219-i11.gif"/></inline-formula> are as in Main Results.</p> |
url |
http://www.advancesindifferenceequations.com/content/2011/237219 |
work_keys_str_mv |
AT xihongjian asymptoticbehaviorofsolutionsofhigherorderdynamicequationsontimescales AT suntaixiang asymptoticbehaviorofsolutionsofhigherorderdynamicequationsontimescales AT pengxiaofeng asymptoticbehaviorofsolutionsofhigherorderdynamicequationsontimescales |
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1716763779470983168 |