Approximate controllability of impulsive semilinear evolution equations in Hilbert spaces

Several dynamical systems in fields such as engineering, chemistry, biology, and physics show impulsive behaviour by reason of unexpected changes at specific times. These behaviours are described by differential systems under impulse effects. The current paper examines approximate controllability for semi-linear impulsive differential and neutral differential equations in Hilbert spaces. By applying a fixed-point method and semigroup theory, a new sufficient condition is provided for the (A-controllability) approximate controllability of neutral and impulsive differential equations (IDEs). To demonstrate the value of the suggested consequences, three examples are presented, offering improvements over some recent findings.

工程、化学、生物及物理等领域的若干动态系统，会因特定时刻的意外变化而呈现脉冲行为。这类行为可通过脉冲效应下的微分系统描述。本文探究了希尔伯特空间（Hilbert spaces）中半线性脉冲微分方程与中立型微分方程（neutral differential equations）的近似能控性（approximate controllability）。通过应用不动点方法（fixed-point method）与半群理论（semigroup theory），本文为中立型及脉冲微分方程（IDEs）的（A-controllability）近似能控性提供了新的充分条件。为验证所得结论的价值，文中给出三个示例，其结果较近期部分研究发现有所改进。