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Pure Mathematics 2026
时滞微分变分不等式的解的存在性
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Abstract:
本文研究了一类具有时滞和变分不等式约束的耦合动力系统解的存在性问题。系统由时滞微分方程和变分不等式耦合构成，在控制理论与工程系统中具有重要应用。通过利用Schauder不动点定理，扩展解方法以及Gronwall不等式等方法，证明了在适当条件下系统解的存在性。
This paper studies the existence of solutions for a class of coupled dynamical systems with time delays and variational inequality constraints. The system is composed of delayed differential equations coupled with variational inequalities and has important applications in control theory and engineering systems. By utilizing the Schauder fixed point theorem, extended solution methods, and the Gronwall inequality, the existence of solutions for the system under appropriate conditions is proven.
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