Nan-jing Huang

A class of impulsive differential variational inequalities in finite dimensional spaces

Abstract In this paper, a new class of impulsive differential variational inequalities (IDVIs) are introduced and studied in finite dimensional Euclidean spaces. Some existence results on the solutions for the IDVIs are presented under suitable conditions and a convergence theorem of the discrete Euler time-dependent procedure for solving the IDVI is proved by using constructed discrete approximation methods for the impulsive differential inclusions (IDIs). The stability results concerned with the solutions of the IDVIs are also considered when the variation of initial data, impulsive perturbation and right-hand sides happens.

Generalized Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems

We introduce and study well-posedness in connection with the symmetric vector quasi-equilibrium problem, which unifies its Hadamard and Levitin-Polyak well-posedness. Using the nonlinear scalarization function, we give some sufficient conditions to guarantee the existence of well-posedness for the symmetric vector quasi-equilibrium problem.