Asymptotic Behavior of Solutions of Higher-Order Dynamic Equations on Time Scales
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چکیده
We investigate the asymptotic behavior of solutions of the following higher-order dynamic equation xΔ n t f t, x t , xΔ t , . . . , xΔ n−1 t 0, on an arbitrary time scale T, where the function f is defined on T × R. We give sufficient conditions under which every solution x of this equation satisfies one of the following conditions: 1 limt→∞x n−1 t 0; 2 there exist constants ai 0 ≤ i ≤ n − 1 with a0 / 0, such that limt→∞x t / ∑n−1 i 0 aihn−i−1 t, t0 1, where hi t, t0 0 ≤ i ≤ n − 1 are as in Main Results.
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تاریخ انتشار 2011