A new periodicity concept for time scales

Details A new periodicity concept for time scales A new periodicity concept for time scales

2010-12-09

arxiv.org/abs/1012.2002v3

Mathematics

Classical Analysis and ODEs

11 pages, Accepted for publication in Mathematica Slovaca, Vol 63, 2013

Scientific paper

By means of the shift operators we introduce a new periodicity concept on time scales. This new approach will enable researchers to investigate periodicity notion on a large class of time scales whose members may not satisfy the condition: "there exists a $P>0$ such that $t\pm P\in\mathbb{T}$ for all $t\in\mathbb{T}$", unlike the existing literature. Therefore, the results of this paper open an avenue for the investigation of periodic solutions of $q$-difference equations.

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