School of Information Engineering, Shandong Management University, Jinan 250357, China.
School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China.
Math Biosci Eng. 2023 Jan;20(2):2061-2080. doi: 10.3934/mbe.2023095. Epub 2022 Nov 14.
This paper investigates a new class of non-autonomous second-order measure evolution systems involving state-dependent delay and non-instantaneous impulses. We introduce a stronger concept of exact controllability called total controllability. The existence of mild solutions and controllability for the considered system are obtained by applying strongly continuous cosine family and the Mönch fixed point theorem. Finally, an example is used to verify the practical application of the conclusion.
本文研究了一类新的非自治二阶测度演化系统，该系统涉及状态相关时滞和非瞬时脉冲。我们引入了一个称为完全可控性的更强的精确可控性概念。通过应用强连续余弦族和 Mönch 不动点定理，得到了所考虑系统的温和解的存在性和可控性。最后，通过一个例子验证了结论的实际应用。
