带时滞项的中立型脉冲微分方程的周期边值问题(英文)

Periodic Boundary Value Problems for Impulsive Neutral Differential Equations with Delay Argument

脉冲微分方程是模拟控制理论、物理学、化学、生物技术、工业机器人等方面的一些过程和现象的一种非常好的模型.本文研究了带时滞项的中立型脉冲微分方程的周期边值问题的极小值与极大值解的存在性.首先引入了方程新的上下解概念,然后发展了一个脉冲不等式.利用它们和单调迭代法,获得了两个新的比较原理,并利用线性化的方法,进一步建立了该方程极值解的一个存在准则,所得主要结果改进和推广了现有文献中的一些结果.最后,举例说明了这个存在准则的有效性.

Recently, the impulsive differential equations are recognized as an excellent source of mod els for simulating processes and phenomena observed in control theory, physics, chemistry, biotechnology, industrial robotics, etc.. In this paper, we study the existence of the minimal and maximal solutions of the periodic boundary value problems for impulsive neutral differential equations with delay argument. First, a new concept of lower and upper solutions of the equations is introduced. Then the impulsive inequality is developed. By using the inequality and the monotone iterative technique, we obtain two new comparison principles, and establish a new existence criterion of extremal solutions for the equations by the linearized technique. Our main result improves and generalizes some well known results in the literature. Finally, an example is given to illustrate the effectiveness of the proposed existence criterion.