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Asymptotic behavior of $n$-th order dynamic equations. (English) Zbl 1279.34106
Summary: We are concerned with the asymptotic behavior of solutions of an $n$th-order linear dynamic equation on a time scale in terms of Taylor monomials. In particular, we describe the asymptotic behavior of the so-called (first) principal solution in terms of the Taylor monomial of degree $n-1$. Several interesting properties of the Taylor monomials are established so that we can prove our main results.

MSC:
34N05Dynamic equations on time scales or measure chains
34A30Linear ODE and systems, general
34D05Asymptotic stability of ODE