A Generalized Wirtinger's Inequality with Applications to a Class of Ordinary Differential Equations
<p/> <p>We first prove a generalized Wirtinger's inequality. Then, applying the inequality, we study estimates for lower bounds of periods of periodic solutions for a class of delay differential equations <inline-formula> <graphic file="1029-242X-2009-710475-i1.gif&quo...
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2009-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2009/710475 |
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doaj-a641bbf071c442f8a6635911cbf6f46b2020-11-24T21:20:19ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2009-01-0120091710475A Generalized Wirtinger's Inequality with Applications to a Class of Ordinary Differential EquationsCheng RongZhang Dongfeng<p/> <p>We first prove a generalized Wirtinger's inequality. Then, applying the inequality, we study estimates for lower bounds of periods of periodic solutions for a class of delay differential equations <inline-formula> <graphic file="1029-242X-2009-710475-i1.gif"/></inline-formula>, and <inline-formula> <graphic file="1029-242X-2009-710475-i2.gif"/></inline-formula>, where <inline-formula> <graphic file="1029-242X-2009-710475-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2009-710475-i4.gif"/></inline-formula>, and <inline-formula> <graphic file="1029-242X-2009-710475-i5.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2009-710475-i6.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2009-710475-i7.gif"/></inline-formula> are two given constants. Under some suitable conditions on <inline-formula> <graphic file="1029-242X-2009-710475-i8.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2009-710475-i9.gif"/></inline-formula>, lower bounds of periods of periodic solutions for the equations aforementioned are obtained.</p>http://www.journalofinequalitiesandapplications.com/content/2009/710475 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Cheng Rong Zhang Dongfeng |
| spellingShingle |
Cheng Rong Zhang Dongfeng A Generalized Wirtinger's Inequality with Applications to a Class of Ordinary Differential Equations Journal of Inequalities and Applications |
| author_facet |
Cheng Rong Zhang Dongfeng |
| author_sort |
Cheng Rong |
| title |
A Generalized Wirtinger's Inequality with Applications to a Class of Ordinary Differential Equations |
| title_short |
A Generalized Wirtinger's Inequality with Applications to a Class of Ordinary Differential Equations |
| title_full |
A Generalized Wirtinger's Inequality with Applications to a Class of Ordinary Differential Equations |
| title_fullStr |
A Generalized Wirtinger's Inequality with Applications to a Class of Ordinary Differential Equations |
| title_full_unstemmed |
A Generalized Wirtinger's Inequality with Applications to a Class of Ordinary Differential Equations |
| title_sort |
generalized wirtinger's inequality with applications to a class of ordinary differential equations |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1025-5834 1029-242X |
| publishDate |
2009-01-01 |
| description |
<p/> <p>We first prove a generalized Wirtinger's inequality. Then, applying the inequality, we study estimates for lower bounds of periods of periodic solutions for a class of delay differential equations <inline-formula> <graphic file="1029-242X-2009-710475-i1.gif"/></inline-formula>, and <inline-formula> <graphic file="1029-242X-2009-710475-i2.gif"/></inline-formula>, where <inline-formula> <graphic file="1029-242X-2009-710475-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2009-710475-i4.gif"/></inline-formula>, and <inline-formula> <graphic file="1029-242X-2009-710475-i5.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2009-710475-i6.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2009-710475-i7.gif"/></inline-formula> are two given constants. Under some suitable conditions on <inline-formula> <graphic file="1029-242X-2009-710475-i8.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2009-710475-i9.gif"/></inline-formula>, lower bounds of periods of periodic solutions for the equations aforementioned are obtained.</p> |
| url |
http://www.journalofinequalitiesandapplications.com/content/2009/710475 |
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