Abstract

This work studies the approximate controllability of a class of first-order retarded semilinear differential equations with delays in control and nonlocal conditions. First we deduce the existence of mild solutions using fixed point approach. For this, the nonlinear function is supposed to be locally Lipschitz, which is a weaker condition than Lipschitz continuity. Controllability results of the system are shown by using the approximate and iterative technique. The results are illustrated by providing an example.

中文翻译：

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具有控制延迟和非局部条件的延迟半线性系统的温和解和近似可控性

摘要

这项工作研究了一类在控制和非局部条件下具有延迟的一阶延迟半线性微分方程的近似可控性。首先，我们使用不动点方法推导出温和解的存在。为此，非线性函数应该是局部 Lipschitz，这是比 Lipschitz 连续性更弱的条件。系统的可控性结果采用近似和迭代技术进行了展示。通过提供一个例子来说明结果。