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Existence and Stability Property of Almost Periodic Solutions in Discrete Almost Periodic Systems

机译：离散概周期系统概周期解的存在性和稳定性

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In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, a_(ij) are almost periodic in n and satisfy a_(ij)(n)≥0 for i≠j,? for 1≤j≤m. In the special case where a_(ij)(n) are constant functions, above system is a mathematical model of gas dynamics and was treated by T. Carleman and R. D. Jenks for differential systems. In the main theorem, we show that if the m X m matrix (a_(ij)(n)) is irreducible, then there exists a positive almost periodic solution which is unique and has some stability. Moreover, we can see that this result gives R. D. Jenks’ result for differential model in the case where a _( ij ) (n) are constant functions. In Section 3, we consider the linear system with variable cofficients . Even in nonlinear problems, this linear system plays an important role, as their variational equations, and it is requested to determine the uniform asymptotically stability of the zero solution from the information about A(n). In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: above linear system and? for 1≤i≤m, respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.
机译：在本文中，我们考虑一个几乎周期的系统，其中包括类型为的系统，其中 k是一个正整数，a_（ij）在n中几乎是周期的，并且对于i满足a_（ij）（n）≥0 ≠j ，？对于1≤j≤m。在a_（ij）（n）是常数函数的特殊情况下，上述系统是气体动力学的数学模型，并由T. Carleman和R. D. Jenks处理了差分系统。在主定理中，我们表明，如果m X m矩阵（a_（ij）（n））是不可约的，则存在一个正周期近似解，它是唯一的并且具有一定的稳定性。此外，我们可以看到，在_（ij）（n）为常数函数的情况下，该结果给出了R. D. Jenks的微分模型结果。在第3节中，我们考虑具有可变系数的线性系统。即使在非线性问题中，该线性系统也起着重要的作用，作为其变分方程，要求从有关A（n）的信息中确定零解的一致渐近稳定性。为了获得线性和非线性几乎周期离散系统的几乎周期解的存在：线性系统之上？对于1≤i≤m，我们将在一定的稳定性属性和对角支配矩阵条件之间进行考虑，这些稳定性属性被称为均匀渐近稳定。

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