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="...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2011-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2011/237219 |
| Summary: | <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> |
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| ISSN: | 1687-1839 1687-1847 |