Existence result for differential variational inequality with relaxing the convexity condition

In this paper, a class of differential variational inequalities are studied, and a new approach is introduced to relax the convexity condition. Firstly, an existence theorem of Carathéodory weak solution for the differential variational inequalities is established. Secondly, an algorithm for solving the problem is developed and the convergence analysis for the algorithm is given. Finally, a numerical example is reported to illustrate the proposed algorithm.