推广的逐段常变量微分方程的Levinson定理
Levinson Theorem for Differential Equations with Piecewise Constant Argument Generalized
摘要：
在这项工作中，它提出了一个适应的渐近定理N。Levinson（1948）提出的分段常变元微分方程，推广到了M. 2007年的艾哈迈德。为了简单起见，不失一般性，考虑了参数延迟的情况。了N. Levinson定理是M. S. P. Eastham在他的工作，这是目前在这个书目。更相关的假设，这一定理的突出，它是建立一个版本的这个定理与这些假设的常微分方程。这种形式是推广到具有分段常数变元的微分方程的形式。这种适应性是通过利用压缩算子构造的Banach不动点来证明的。
英文摘要：
In this work, it is presented an adaptation of an asymptotic theorem of N. Levinson of 1948, to differential equation with piecewise constant argument generalized, which were introduced by M. Akhmet in 2007. By simplicity and without loss of generality, the case where the argument is delayed is considered. The N. Levinson's theorem which is adapted is that dealt by M. S. P. Eastham in his work which is present in this bibliography. The more relevant hypotheses of this theorem are highlighted an it is established a version of this theorem with these hypotheses for ordinary differential equations. Such a version is that which is adapted to differential equation with piecewise constant argument generalized. The adaptation is proved by mean the Banach fixed point where contractive operator is built form a suitable version of the constant variation formula.
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