Qualitative analysis of dynamic equations on time scales
作者: Syed Abbas
作者单位: 1Indian Institute of Technology Mandi, Kamand, India
刊名: Electronic Journal of Differential Equations, 2018, Vol.2018 (51,), pp.1-13
来源数据库: Directory of Open Access Journals
关键词: Dynamic equationsTime scale calculusWeierstrass M-testUniform convergencePicard's iterationEpsilon-approximate solution
原始语种摘要: In this article, we establish the Picard-Lindelof theorem andapproximating results for dynamic equations on time scale.We present a simple proof for the existence and uniqueness of thesolution. The proof is produced by using convergence and Weierstrass M-test.Furthermore, we show that the Lispchitz condition is not necessary foruniqueness. The existence of epsilon-approximate solution is establishedunder suitable assumptions. Moreover, we study the approximate solutionof the dynamic equation with delay by studying the solution of thecorresponding dynamic equation with piecewise constant argument.We show that the exponential stability is preserved in such approximations.
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  • scales 天平
  • approximate 近似的
  • dynamic 动力学的
  • exponential 指数的
  • piecewise 分段
  • iteration 迭代
  • proof 证明
  • convergence 汇合
  • epsilon 小的正数
  • simple 单纯的