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Existence of periodic solutions of dynamic equations on time scales by averaging



The first author was supposed by NSFC (grant No. 11301541). The second author was supposed by National Basic Research Program of China (grant No. 2013CB834100), NSFC (grant No. 11571065), NSFC (grant No. 11171132). The fourth author was supposed by NSFC (grant No. 11201173)

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  • In this paper, we study the existence of periodic solutions for perturbed dynamic equations on time scales. Our approach is based on the averaging method. Further, we extend some averaging theorem to periodic solutions of dynamic equations on time scales to $k-$th order in $\varepsilon$. More precisely, results of higher order averaging for finding periodic solutions are given via the topological degree theory.

    Mathematics Subject Classification: Primary: 34C25, 34N05; Secondary: 70K65.


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