Existence of Three Solutions for Hemi-variational Inequalities Driven With Impulsive Effects

In this paper we prove the existence of at least three solutions to the following second-order impulsive system:   where `A: [0, T] rightarrow mathbb{R}^{N times N}` is a continuous map from the interval `[0, T]` to the set of `N`-order symmetric matrixes. The approach is fully based on a recent three critical points theorem of Teng [K. Teng, Two nontrivial solutions for hemivariational inequalities driven by nonlocal elliptic operators, Nonlinear Anal. (RWA) 14 (2013) 867-874].