In this paper, we consider a dynamical system for solving equilibrium problems in the framework of Hilbert spaces. First, we prove that under strong pseudo-monotonicity and Lipschitz-type continuity assumptions, the dynamical system has a unique equilibrium solution, which is also globally exponentially stable. Then, we derive the linear rate of convergence of a discrete version of the proposed dynamical system to the unique solution of the problem. Global error bounds are also provided to estimate the distance between any trajectory and this unique solution. Some numerical experiments are reported to confirm the theoretical results.

中文翻译：

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强拟单调平衡问题的动力学系统

在本文中，我们考虑在希尔伯特空间框架内解决平衡问题的动力系统。首先，我们证明了在强伪单调性和 Lipschitz 型连续性假设下，动力系统具有唯一的平衡解，并且也是全局指数稳定的。然后，我们推导出所提出的动态系统的离散版本对问题的唯一解的线性收敛率。还提供了全局误差界限来估计任何轨迹与此唯一解决方案之间的距离。报告了一些数值实验来证实理论结果。