A second-order dynamical system for equilibrium problems

We consider a second-order dynamical system for solving equilibrium problems in Hilbert spaces. Under mild conditions, we prove existence and uniqueness of strong global solution the proposed system. establish exponential convergence trajectories under pseudo-monotonicity Lipschitz-type conditions. then investigate discrete version system, which leads to fixed point-type algorithm with inertial effect relaxation. The linear this is established suitable conditions on parameters. Finally, some numerical experiments are reported confirming theoretical results.