Periodic boundary value problems for fırst order dynamic equations on time scales

Zhang, Xiaozhi; Zhu, Chuanxi

doi:10.1186/1687-1847-2012-76

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Cited by 3 publications

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“…Lots of excellent books, monographs and research papers are available in this field majorally contributed by Martin Bohner, Allan Peterson, Lynn Erbe, Ravi P. Agarwal, Samir H. Saker, Zhenlai Han, Qi Ru Wang, Youssef N. Raffoul and many more, we refer to [1,2,4,6,10,11,12,13,14,16,17,18,19,22,23,25,31,32,33,34,37,38,39,40] and references therein. The books [8,21] present a complete discussion on time scale calculus.…”

Section: Introductionmentioning

confidence: 99%

Qualitative analysis of dynamic equations on time scales

Abbas

2017

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In this paper, we establish the Picard-Lindelöf theorem and approximating results for dynamic equations on time scale. We present a simple proof for the existence and uniqueness of the solution. The proof is produced by using convergence and Weierstrass M-test. Furthermore, we show that the Lispchitz condition is not necessary for uniqueness. The existence of ǫ−approximate solution is established under suitable assumptions. Moreover, we study the approximate solution of the dynamic equation with delay by studying the solution of the corresponding dynamic equation with piecewise constant argument. We show that the exponential stability is preserved in such approximations.

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