A class of delay differential variational inequalities with boundary conditions

Abstract

In this paper, we introduce a new class of delay differential variational inequalities. Delay differential variational inequalities with initial conditions have been already introduced and studied in literatures. The novelty of this work is to consider such problems with boundary conditions. In the first step, we prove a result on the existence of solutions for delay differential variational inequalities with boundary conditions. In the second step, we study the numerical aspect of the problem, where a numerical scheme is considered and the convergence analysis for the approach is provided. As an application, we consider dynamic Nash equilibrium with time delay. A numerical illustration is provided by considering the problem of optimal allocation of distributed generations.