Asymptotic Behavior of Solutions of Higher-Order Dynamic Equations on Time Scales

• Main Authors: Xi Hongjian, Sun Taixiang, Peng Xiaofeng
• Format: Article
• Language: English
• Published: SpringerOpen 2011-01-01
• Series: Advances in Difference Equations
• Online Access: http://www.advancesindifferenceequations.com/content/2011/237219

<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>