Almost automorphic solutions of dynamic equations on time scales
Almost automorphic solutions of dynamic equations on time scales
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DOI：
10.1016/j.jfa.2013.06.013
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发表时间：
2013-11
影响因子：
1.7
通讯作者：
C. Lizama;J. Mesquita
中科院分区：
文献类型：
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作者：
C. Lizama;J. Mesquita
本文引入了时标上几乎自守函数的概念，并给出了关于其基本性质的第一个结果。然后，我们研究了时标上的非自治动力方程x Δ（t）= A（t）x（t）+ f（t）和x Δ（t）= A（t）x（t）+ g（t，x（t）），t∈ T，其中T是本文定义的时标的一个特例.我们证明了一个结果，确保两个方程的几乎自守解的存在性，假设该系统的相关齐次方程承认指数二分法。在函数g满足整体Lipschitz型条件的条件下，证明了时标上非线性动力方程概自守解的存在唯一性.此外，我们提出了我们的结果的一些新的几乎自守的时间尺度的应用。最后，我们提出了一些有趣的模型，我们的主要结果可以应用。
In the present work, we introduce the concept of almost automorphic functions on time scales and present the first results about their basic properties. Then, we study the nonautonomous dynamic equations on time scales given by x Δ (t)= A (t) x (t)+ f (t) and x Δ (t)= A (t) x (t)+ g (t, x (t)), t∈ T where T is a special case of time scales that we define in this article. We prove a result ensuring the existence of an almost automorphic solution for both equations, assuming that the associated homogeneous equation of this system admits an exponential dichotomy. Also, assuming that the function g satisfies the global Lipschitz type condition, we prove the existence and uniqueness of an almost automorphic solution of the nonlinear dynamic equation on time scales. Further, we present some applications of our results for some new almost automorphic time scales. Finally, we present some interesting models in which our main results can be applied.