时滞微分变分不等式的解的存在性
Existence of Solutions for Time-Delay Differential Variational Inequalities
DOI: 10.12677/pm.2026.161020, PDF,   
作者: 许界科：成都理工大学数学科学学院，四川 成都
关键词: 时滞系统；变分不等式；存在性；不动点定理；Time-Delay Systems； Variational Inequalities； Existence； Fixed Point Theorem
摘要: 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。
Abstract: 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.
文章引用：许界科. 时滞微分变分不等式的解的存在性[J]. 理论数学, 2026, 16(1): 173-179. https://doi.org/10.12677/pm.2026.161020

参考文献

[1] Facchinei, F. and Pang, J.S. (2003) Finite Dimensional Variational Inequalities and Complementarity Problems. Springer.
[2] Chen, X. and Wang, Z. (2014) Differential Variational Inequality Approach to Dynamic Games with Shared Constraints. Mathematical Programming, 146, 379-408. [Google Scholar] [CrossRef] 
[3] Chen, T., Huang, N. and Sofonea, M. (2022) A Differential Variational Inequality in the Study of Contact Problems with Wear. Nonlinear Analysis: Real World Applications, 67, Article 103619. [Google Scholar] [CrossRef] 
[4] 傅朝金, 廖晓昕. 时滞微分方程的稳定性[J]. 数学物理学报, 2003, 23(4): 494-498.
[5] 张石生. 变分不等式及其相关问题[M]. 重庆: 重庆科学技术出版社, 2008.
[6] 孙炯, 贺飞, 郝晓玲, 等. 泛函分析[M]. 第二版. 北京: 高等教育出版社, 2010.
[7] Chen, X. and Wang, Z. (2013) Convergence of Regularized Time-Stepping Methods for Differential Variational Inequalities. SIAM Journal on Optimization, 23, 1647-1671. [Google Scholar] [CrossRef] 
[8] Smart, D.R. (1973) Fixed Point Theorems. Cambridge University Press.
[9] Hirsch, M.W., Smale, S. and Devaney, R.L. (2004) Differential Equations, Dynamical Systems, and an Introduction to Chaos. Academic Press.
[10] Rudin, W. (1970) Real and Complex Analysis. The McGraw-Hill Companies, Inc.
[11] Crouzeix, J. (1997) Pseudomonotone Variational Inequality Problems: Existence of Solutions. Mathematical Programming, 78, 305-314. [Google Scholar] [CrossRef] 
[12] Dinculeanu, N. (2000) Vector Integration and Stochastic Integration in Banach Spaces. Wiley. [Google Scholar] [CrossRef] 
[13] Yosida, K. (1980) Functional Analysis. Springer.
[14] Lang, S. (1993) Real and Functional Analysis. Springer.

为你推荐