Differential variational-hemivariational inequalities with unbounded perturbations and memory effects

Inspired by a nonlinear elastic-mass-damper vibration system incorporating frictional contact effects, in this paper we consider two types of differential inclusions. These inclusions are characterized by memory effects and unbounded perturbations assumed to satisfy a truncated Lipschitz condition tailored for multi-valued mappings with unbounded values. By invoking Schauder's fixed point theorem, we prove the existence of solutions to our two inclusions. In addition, we establish an approximation-type relaxation property for them.