Simple Floquet Theory on Time Scales

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Authors

ADAMEC Ladislav

Year of publication 2005
Type Article in Proceedings
Conference Proc. of the Eight Internat. Conf. on Difference Equations and Applications
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords key words
Description The author proves the following theorem. Let $a(t)$ be rd-continuous and regressive on a $T$-periodic time scale $\Bbb T$(with a minor restriction on $\Bbb T$). Then any nontrivial solution $\phi(t)$ of the first order time scale equation $x^\Delta=a(t)\,x$ has the form $\phi(t)=p(t)\,e_b(t,t_0)$ on $\Bbb T$, where $b>0$, $p(t+2T)=p(t)$ on $\Bbb T$, and $e_b(t,t_0)$ is the time scale exponential function.
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