一类时滞微分变分不等式的解的存在性
Existence of Solutions to a Class of Time-Delay Differential Variational Inequalities
DOI: 10.12677/pm.2026.167170, PDF,   
作者: 赵 文：中国电子科技集团公司第三十研究所，四川 成都；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 System； Variational Inequality； Existence； Fixed-Point Theorem
摘要: 本文研究一类由时滞微分方程与变分不等式耦合构成的动力系统解的存在性问题。该类系统在控制理论与工程系统中具有重要应用背景。利用Schauder不动点定理、扩展解方法及变分不等式相关理论，在适当假设条件下证明了系统解的存在性，并进一步分析了其解的结构特征。
Abstract: This paper studies the existence of solutions to a class of dynamical systems coupled with time-delay differential equations and variational inequalities. These systems have important applications in control theory and engineering systems. Using Schauder’s fixed-point theorem, the extended solution method, and related theories of variational inequalities, the existence of system solutions is proved under appropriate assumptions, and the structural characteristics of the solutions are further analyzed.
文章引用：赵文, 许界科. 一类时滞微分变分不等式的解的存在性[J]. 理论数学, 2026, 16(7): 27-33. https://doi.org/10.12677/pm.2026.167170

参考文献

[1] Pang, J. and Stewart, D.E. (2008) Differential Variational Inequalities. Mathematical Programming, 113, 345-424. [Google Scholar] [CrossRef] 
[2] Chen, X. and Wang, Z.Y. (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 ID: 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2版. 北京: 高等教育出版社, 2010.
[7] Chen, X.J. and Wang, Z.Y. (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] Facchinei, F. and Pang, S.J. (2003) Finite-Dimensional Variational Inequalities and Complementarity Problems, Volume I. Springer. [Google Scholar] [CrossRef] 
[12] Crouzeix, J. (1997) Pseudomonotone Variational Inequality Problems: Existence of Solutions. Mathematical Programming, 78, 305-314. [Google Scholar] [CrossRef] 
[13] Dinculeanu, N. (2000) Vector Integration and Stochastic Integration in Banach Spaces. John Wiley & Sons. [Google Scholar] [CrossRef] 
[14] Yosida, K. (1980) Functional Analysis. Springer.
[15] Lang, S. (1993) Real and Functional Analysis. Springer. [Google Scholar] [CrossRef] 

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